{"id":1260,"date":"2019-09-26T21:06:30","date_gmt":"2019-09-26T13:06:30","guid":{"rendered":"https:\/\/0.mnihyc.com\/blog\/?p=1260"},"modified":"2020-02-09T02:12:18","modified_gmt":"2020-02-08T18:12:18","slug":"yzoj-p4611-%e5%8c%ba%e9%97%b4%e5%8a%a0%e5%a4%9a%e9%a1%b9%e5%bc%8f%ef%bc%88yjc-%e7%9a%84%e6%95%b0%e7%bb%84-%e5%a4%9a%e9%a1%b9%e5%bc%8f%ef%bc%9f%ef%bc%89","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/1260","title":{"rendered":"YZOJ P4611 \u533a\u95f4\u52a0\u591a\u9879\u5f0f\uff08YJC \u7684\u6570\u7ec4\/\u591a\u9879\u5f0f\uff1f\uff09"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P4611 \u533a\u95f4\u52a0\u591a\u9879\u5f0f\uff08YJC \u7684\u6570\u7ec4\/\u591a\u9879\u5f0f\uff1f\uff09<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a4444MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a1048576KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #993300;\">\\(7.2\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7531\u4e8e\u672c\u9898\u4e4b\u524d\u88ab*\u4e86\uff0c\u6240\u4ee5\u73b0\u5728\u6570\u636e\u5c31\u662f\u968f\u4fbf\u9020\u7684<span style=\"color: #ffffff;\">\uff0c\u53ef\u80fd\u4f1a\u56e0\u4e3a\u592a\u6c34\u53c8\u88ab\u8279 \u00a0\u00a0\u00a0\u00a0\/\/\u7ed9\u51fa\u9898\u4eba\u7559\u70b9\u9762\u5b50\u5427qwq<\/span><\/p>\n<p>YJC \u5728 <strong>AK<\/strong> \u4e86\u4e00\u573a\u6821\u5185\u4e4b\u540e\uff0c\u5bf9\u5176\u4e2d\u7684\u4e00\u9898\uff08P2036 \u300cA Simple Data Structure Problem II \u300d\uff09\u4ea7\u751f\u4e86\u5174\u8da3\u3002<\/p>\n<p>\u4e8e\u662f\u4ed6\u51fa\u4e86\u4e00\u9898\u52a0\u5f3a\u7248\uff08P4316 \u300cASDSP VII \u2014\u2014 YJC\u6811\u300d\uff09\uff0c\u7136\u800c\uff0c\u4ed6\u8fd8\u662f\u89c9\u5f97\u8fd9\u4e2a\u52a0\u5f3a\u7248<strong>\u592a\u7b80\u5355<\/strong>\u5566\uff01\uff01\uff01<\/p>\n<p>\u6240\u4ee5\uff0c\u8fd9\u6b21\uff0c\u4ed6\u4e0d\u4ec5\u628a \\(K \\leq 5\\) \u5f80\u540e\u9762\u52a0\u4e86<strong>\u4e09\u4e2a\u96f6<\/strong>\u53d8\u6210\u4e86 \\(K \\leq 5000\\) \uff0c\u8fd8\u5bf9\u8be2\u95ee\u505a\u4e86\u4e00\u70b9\u4fee\u6539\uff01<\/p>\n<p>\u559c\u6b22<strong>\u5dee\u5206<\/strong>\u7684 YJC \u6709\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(N\\) \u7684\u6570\u7ec4 \\(c\\)\uff0c\u521d\u59cb\u503c\u90fd\u4e3a \\(0\\)\uff0c\u4e0b\u6807\u7f16\u53f7\u4e3a \\(1, 2, \\cdots, N\\) \u3002<\/p>\n<p>\u73b0\u5728 YJC \u5fd9\u7740 AK CSP-S2019\uff0c\u6ca1\u7a7a\u9a8c\u8bc1\u6570\u636e\u7684\u6b63\u786e\u6027\uff0c\u6240\u4ee5\u53ea\u80fd\u628a\u8fd9\u4e2a\u91cd\u4efb\u4ea4\u7ed9\u4e86\u4f60 \u2014\u2014 ******\uff0c\u5e0c\u671b\u4f60\u80fd\u5199\u4e00\u4e2a\u7a0b\u5e8f\u5e2e\u4ed6\u5b9e\u73b0\u4ee5\u4e0b\u7684\u51e0\u4e2a\u64cd\u4f5c\uff1a<\/p>\n<p>\\(opt=1\\)\uff0c\u7ed9\u5b9a \\(L, R\\)\uff0c\u8f93\u51fa \\(\\sum\\limits_{i=L}^R c_i\\) \u7684\u503c\u5bf9 \\(998244353\\) \u53d6\u6a21\u540e\u7684\u7ed3\u679c\uff1b<\/p>\n<p>\\(opt=0\\)\uff0c\u7ed9\u5b9a \\(L, R\\) \u4ee5\u53ca \\(K\\) \u6b21\u591a\u9879\u5f0f \\(f(x)=\\sum\\limits_{k=0}^K a_kx^k\\)\uff0c\u5bf9 \\(c_L, c_{L+1}, \\cdots, c_R\\) \u5206\u522b\u52a0\u4e0a \\(f(1), f(2), \\cdots, f(R-L+1)\\) \u7684\u503c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u4e24\u4e2a\u6b63\u6574\u6570 \\(N, Q\\) \uff0c\u5206\u522b\u8868\u793a\u533a\u95f4\u8303\u56f4 \\([1, N]\\) \u53ca\u8be2\u95ee\u6570 \\(Q\\) \u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6bcf\u884c\uff08\u9664\u4e86\u6bcf\u4e2a \\(opt=0\\) \u64cd\u4f5c\u7684\u4e0b\u4e00\u884c\uff09\u7684\u7b2c\u4e00\u4e2a\u6570 \\(opt\\) \u8868\u793a\u64cd\u4f5c\u7c7b\u578b\u3002<\/p>\n<p>\u82e5 \\(opt=0\\)\uff0c\u5219\u63a5\u4e0b\u6765\u6709\u4e24\u4e2a\u6b63\u6574\u6570 \\(L, R\\) \u8868\u793a\u64cd\u4f5c\u7684\u533a\u95f4 \\([L, R]\\)\u3002\u7d27\u63a5\u7740\u4e0b\u4e00\u884c\u7684\u7b2c\u4e00\u4e2a\u6574\u6570 \\(K\\) \u8868\u793a\u591a\u9879\u5f0f\u7684\u6700\u9ad8\u6b21\u6570\u4e3a \\(K\\) \uff0c\u63a5\u4e0b\u6765 \\(K+1\\) \u4e2a\u6574\u6570 \\(a_0, a_1, \\cdots, a_K\\) \u5206\u522b\u8868\u793a\u591a\u9879\u5f0f\u00a0\\(f(x)= \\displaystyle\\sum\\limits_{k=0}^K a_kx^k\\) \u7684\u7cfb\u6570\uff1b<\/p>\n<p>\u82e5 \\(opt=1\\)\uff0c\u5219\u63a5\u4e0b\u6765\u6709\u4e24\u4e2a\u6b63\u6574\u6570 \\(L, R\\) \u8868\u793a\u8be2\u95ee\u7684\u533a\u95f4 \\([L, R]\\)\u3002<\/p>\n<p>\u56e0\u4e3a YJC \u5fd9\u7740 AK CSP-S2019\uff08\u4e4b\u524d\u8bf4\u8fc7\u4e86\uff09\uff0c\u6240\u4ee5\u4ed6\u4e00\u4e0d\u5c0f\u5fc3\u628a\u6570\u636e\u7ed9<strong>\u52a0\u5bc6<\/strong>\u4e86\u3002<\/p>\n<p>\u8bb0 \\(lastans\\) \u4e3a\u4e0a\u4e00\u4e2a \\(opt=1\\) \u8be2\u95ee\u8f93\u51fa\u7684\u7b54\u6848\uff08\u6ca1\u6709\u5219\u4e3a \\(0\\)\uff09\uff1a\u5bf9\u4e8e\u8bfb\u5165\u7684 \\(L\\) \u548c \\(R\\)\uff0c\\(L \\;\\mbox{xor} \\left(lastans^2\\right)\\) \u53ca \\(R \\;\\mbox{xor} \\left(lastans^2\\right)\\) \u5206\u522b\u4e3a\u771f\u5b9e\u7684 \\(L\\) \u548c \\(R\\)\uff1b\u5bf9\u4e8e\u8bfb\u5165\u7684 \\(a_k \\left(0 \\leq k \\leq K\\right)\\)\uff0c\\(a_k \\;\\mbox{xor}\\; lastans\\) \u4e3a\u771f\u5b9e\u7684 \\(a_k\\)\u3002\\(\\mbox{xor}\\) \u8868\u793a\u4e8c\u8fdb\u5236\u4e0b\u7684\u5f02\u6216\u64cd\u4f5c\u3002<\/p>\n<p>\uff08\u53cb\u60c5\u63d0\u793a\uff1a\u6570\u636e\u8303\u56f4\u4fdd\u8bc1\u7684\u662f<strong>\u771f\u5b9e\u7684\u8f93\u5165\u6570\u636e<\/strong>\u7684\u8303\u56f4\u3002\uff09<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a \\(opt=1\\) \u64cd\u4f5c\uff0c\u8f93\u51fa\u4e00\u884c\u4e00\u4e2a\u6570\u8868\u793a\u7b54\u6848\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">10 5\r\n1 9 9\r\n0 8 9\r\n0 1 \r\n1 9 10\r\n0 3 8\r\n2 0 0 0 \r\n1 8 11\r\n<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">0\r\n1\r\n74\r\n<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8bf4\u660e<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u521d\u59cb \\(c_9\\) \u4e3a \\(0\\) \uff0c\u8f93\u51fa \\(0\\)\uff1b<\/p>\n<p>\u5bf9 \\([8, 9]\\) \u52a0\u4e0a \\(f(x)=1\\) \uff1b<\/p>\n<p>\u73b0\u5728 \\(c_9\\) \u4e3a \\(1\\) \uff0c\u8f93\u51fa \\(1\\)\uff1b<\/p>\n<p>\\(lastans=1\\)\uff0c\u771f\u5b9e\u7684 \\(L=3 \\;\\mbox{xor} \\left(1^2\\right)=2\\)\uff0c\\(R=8 \\;\\mbox{xor} \\left(1^2\\right)=9\\)\uff0c\\(a_0=a_1=a_2=0 \\;\\mbox{xor}\\; 1=1\\) \uff0c\u5373\u5bf9 \\([2, 9]\\) \u52a0\u4e0a \\(f(x)=1+x+x^2\\) \uff1b<\/p>\n<p>\\(lastans=1\\)\uff0c\u771f\u5b9e\u7684 \\(L=8 \\;\\mbox{xor} \\left(1^2\\right)=9\\)\uff0c\\(R=11 \\;\\mbox{xor} \\left(1^2\\right)=10\\)\uff0c\u5373\u8be2\u95ee \\(c_9+c_{10}\\)\uff0c\u8f93\u51fa \\(\\left(1+1+8+8^2\\right)+0=74\\)\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u672c\u9898\u91c7\u7528<strong>\u5b50\u4efb\u52a1<\/strong>\u5236\uff0c\u5373\u53ea\u6709\u901a\u8fc7\u4e86\u8be5\u5b50\u4efb\u52a1\u4e0b\u7684\u6240\u6709\u6d4b\u8bd5\u70b9\uff0c\u624d\u80fd\u5f97\u5230\u5176\u76f8\u5e94\u7684\u5206\u6570\u3002<\/p>\n<p>\u5bf9\u4e8e\u6240\u6709\u7684\u6d4b\u8bd5\u70b9\uff0c\u6709 \\(1 \\leq N \\leq 10^{18}\\)\uff0c\\(0 \\leq Q \\leq 100000\\)\uff0c\\(0 \\leq K \\leq 5000\\)\uff1b<\/p>\n<p>\\(1 \\leq L \\leq R \\leq N\\)\uff0c\\(\\forall i \\in [0, K]: 0 \\leq \\left|a_i\\right| &lt; 998244353\\)\u3002<\/p>\n<p>\u8bbe\u6bcf\u4e2a \\(opt=0\\) \u64cd\u4f5c\u7684 \\(K\\) \u5206\u522b\u4e3a \\(k_1, k_2, \\cdots, k_s\\) \uff0c\u8bb0 \\(tk = \\displaystyle\\sum\\limits_{i=1}^s {\\left(k_i+1\\right)}\\)\u3002<\/p>\n<p>\u540c\u65f6\u8bb0 \\(opt=1\\) \u64cd\u4f5c\u7684\u603b\u6b21\u6570\u4e3a \\(tq\\) \u3002<\/p>\n<h4>Subtask 1 \uff08\\(1pts\\)\uff09<\/h4>\n<p>\\(N \\leq 10^5\\)\uff0c\\(K \\leq 0\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk, tq \\leq 50500\\)\u3002<\/p>\n<h4>Subtask 2 \uff08\\(2pts\\)\uff09<\/h4>\n<p>\\(K \\leq 0\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk, tq \\leq 50500\\)\u3002<\/p>\n<h4>Subtask 3 \uff08\\(3pts\\)\uff09<\/h4>\n<p>\\(N \\leq 10^5\\)\uff0c\\(K \\leq 1\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk \\leq 75500\\)\uff0c\\(tq \\leq 50500\\)\u3002<\/p>\n<h4>Subtask 4 \uff08\\(4pts\\)\uff09<\/h4>\n<p>\\(K \\leq 1\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk \\leq 65000\\)\uff0c\\(tq \\leq 50550\\)\u3002<\/p>\n<h4>Subtask 5 \uff08\\(5pts\\)\uff09<\/h4>\n<p>\\(N \\leq 10^5\\)\uff0c\\(K \\leq 2\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk \\leq 84000\\)\uff0c\\(tq \\leq 50500\\)\u3002<\/p>\n<h4>Subtask 6 \uff08\\(6pts\\)\uff09<\/h4>\n<p>\\(K \\leq 2\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk \\leq 100000\\)\uff0c\\(tq \\leq 10500\\)\u3002<\/p>\n<h4>Subtask 7 \uff08\\(7pts\\)\uff09<\/h4>\n<p>\\(N \\leq 10^5\\)\uff0c\\(K \\leq 5\\)\uff0c\\(Q \\leq 100000\\)\uff0c\\(tk \\leq 175785\\)\uff0c\\(tq \\leq 49884\\)\u3002<\/p>\n<h4>Subtask 8 \uff08\\(8pts\\)\uff09<\/h4>\n<p>\\(K \\leq 5\\)\uff0c\\(Q \\leq 80000\\)\uff0c\\(tk \\leq 110000\\)\uff0c\\(tq \\leq 80000\\)\u3002<\/p>\n<h4>Subtask 9 \uff08\\(24pts\\)\uff09<\/h4>\n<p>\\(K \\leq 500\\)\uff0c\\(Q \\leq 1000\\)\uff0c\\(tk \\leq 220000\\)\uff0c\\(tq \\leq 250\\)\u3002<\/p>\n<h4>Subtask 10 \uff08\\(35pts\\)\uff09<\/h4>\n<p>\\(K \\leq 5000\\)\uff0c\\(Q \\leq 75\\)\uff0c\\(tk \\leq 150000\\)\uff0c\\(tq \\leq 50\\)\u3002<\/p>\n<h4>Subtask 11 \uff08\\(5pts\\)\uff09<\/h4>\n<p>\\(K = 5000\\)\uff0c\\(Q \\leq 50\\)\u3002<\/p>\n<p>\u5982\u679c\u662f\u6839\u636e\u6570\u636e\u8303\u56f4\u9009\u62e9\u505a\u6cd5\u7684w\u4e5f\u5361\u4e0d\u4e86\u4e86qaq<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u533a\u95f4\u52a0\u591a\u9879\u5f0f \u53ca \u533a\u95f4\u67e5\u8be2\u3002<\/p>\n<p>\u672c\u6765\u53ea\u6709\u5355\u70b9\u67e5\u8be2\u7684\uff0c\u7ed3\u679c\u88ab L****n * \u8fc7\u53bb\u4e86\uff0c\u7136\u540e\u5c31\u53d8\u6210\u4e86\u96be\u53d7\u7684\u533a\u95f4\u67e5\u8be2\uff09<\/p>\n<p>\u672c\u6765\u6240\u6709\u7684 \\(Q\\) \u90fd\u662f \\(\\leq 50\\) \u7684\uff0c\u7ed3\u679c\u88ab *agoo* * \u8fc7\u53bb\u4e86\uff0c\u7136\u540e\u5c31\u53d8\u6210\u4e86\u96be\u53d7\u7684 \\(Q\\) \u548c \\(K\\) \u6210\u53cd\u6bd4\uff09<\/p>\n<p>\u5982\u679c \\(N, K\\) \u6bd4\u8f83\u5c0f\u7684\u8bdd\u53ef\u4ee5\u8003\u8651\u79bb\u7ebf\u5dee\u5206\uff0c\u5f00\u591a\u4e2a\u6811\u72b6\u6570\u7ec4\u7ef4\u62a4\u3002\u4f46\u662f\u672c\u9898\u4e2d \\(N, K\\) \u90fd\u8f83\u5927\uff0c\u5e76\u4e14\u5f3a\u5236\u5728\u7ebf\uff0c\u9700\u8981\u53e6\u5bfb\u51fa\u8def\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u8003\u8651\u82e5\u4fee\u6539\u7684\u533a\u95f4\u5747\u4e3a \\([1, R]\\)\uff0c\u90a3\u4e48\u5b9e\u9645\u4e0a\u53ea\u9700\u8981\u7ef4\u62a4\u8fd9\u4e9b\u591a\u9879\u5f0f\u5bf9\u5e94\u6b21\u6570\u7684\u7cfb\u6570\u548c\u5373\u53ef\u3002\u56e0\u4e3a \\(c_i\\) \u4e0e \\(f(i)\\) \u5bf9\u5e94\uff0c\u6240\u4ee5\u5bf9\u4e8e\u76f8\u540c\u7684 \\(i^k\\) \u5176\u7cfb\u6570\u53ef\u4ee5<strong>\u5408\u5e76<\/strong>\u3002<\/p>\n<p>\u6240\u4ee5\u53ef\u4ee5\u628a \\(c_i\\) \u770b\u6210\u4e00\u4e2a<strong>\u591a\u9879\u5f0f \\(g(x)\\) \u5728 \\(x=i\\) \u5904\u7684\u503c<\/strong>\uff0c\u4e14 \\(g(x)\\) \u7684\u5404\u9879\u7cfb\u6570\u4e3a\u8fd9\u4e9b\u591a\u9879\u5f0f\u7684\u5bf9\u5e94\u6b21\u6570\u7684<strong>\u7cfb\u6570\u548c<\/strong>\u3002<\/p>\n<p>\u5373\u82e5\u8981\u52a0\u5165\u4e00\u4e2a\u591a\u9879\u5f0f \\(f(x)\\)\uff0c\u56e0\u4e3a \\(c_i\\) \u9700\u8981\u52a0\u4e0a \\(f(i)\\)\uff0c\u800c \\(c_i = g(i)\\)\uff0c\u6240\u4ee5\u76f4\u63a5\u628a \\(g(x)\\) \u7684\u5404\u9879\u7cfb\u6570\u52a0\u4e0a \\(f(x)\\) \u7684\u5bf9\u5e94\u6b21\u6570\u7684\u7cfb\u6570\u5373\u53ef\uff1b<\/p>\n<p>\u82e5\u8981\u67e5\u8be2\u67d0\u4e00\u4e2a \\(c_i\\) \u7684\u503c\uff0c\u53ea\u9700\u8981\u6c42\u51fa \\(g(x)\\) \u7684\u6bcf\u9879\u7cfb\u6570\u7136\u540e\u628a \\(x=i\\) \u5e26\u5165\u5373\u53ef\u3002<\/p>\n<p>\u7531\u4e8e \\(K \\leq 5000\\)\uff0c\u6240\u4ee5\u53ef\u4ee5\u5f00 \\(K\\) \u68f5\u52a8\u6001\u5f00\u70b9<strong>\u7ebf\u6bb5\u6811<\/strong>\u5206\u522b\u7ef4\u62a4\u6bcf\u4e2a \\(g(x)\\) \u7684\u5bf9\u5e94\u9879\u7cfb\u6570\uff0c\u652f\u6301<strong>\u533a\u95f4\u4fee\u6539<\/strong>\u548c<strong>\u5355\u70b9\u67e5\u8be2<\/strong>\u5373\u53ef\u3002<\/p>\n<p>\u7136\u800c\u73b0\u5728\u8981\u4fee\u6539\u7684\u533a\u95f4\u4e3a \\([L, R]\\)\uff0c\u5373 \\(c_i\\) \u4e0e \\(f\\left(i-L+1\\right)\\) \u5bf9\u5e94\uff0c\\(i^k\\) \u4e0e \\(\\left(i-L+1\\right)^k\\) \u4e0d\u540c\u6240\u4ee5\u7cfb\u6570\u65e0\u6cd5\u76f4\u63a5\u5408\u5e76\u3002<\/p>\n<p>\u6240\u4ee5\u8fd9\u91cc\u6709\u4e00\u4e2a\u7b80\u5355\u7c97\u66b4\u529e\u6cd5\uff0c\u53ef\u4ee5<strong>\u5e73\u79fb \\(f(x)\\)<\/strong> \u5f3a\u884c\u4f7f\u5f97 \\(c_i\\) \u4e0e \\(f(i)\\) \u5bf9\u5e94\uff0c\u7136\u540e\u5c31\u53ef\u4ee5\u76f4\u63a5\u5408\u5e76\u4e86\u3002<\/p>\n<p>\u539f\u672c \\(c_i\\) \u4e0e \\(f\\left(i-L+1\\right)\\) \u5bf9\u5e94\uff0c\u8981\u4f7f \\(c_i\\) \u4e0e \\(f(i)\\) \u5bf9\u5e94\uff0c\u6240\u4ee5<strong>\u628a \\(f(x)\\) \u5e73\u79fb\u6210 \\(f(x-L+1)\\)<\/strong>\uff0c\u8fd9\u6837\u5e26\u5165 \\(x=i\\) \u662f\u5f97\u5230\u7684\u5c31\u662f \\(f(i-L+1)\\) \u7684\u503c\u4e86\u3002<\/p>\n<p>\u5373\u82e5 \\(f(x) = \\displaystyle\\sum\\limits_{k=0}^K a_kx^k\\)\uff0c\u90a3\u4e48\u5e73\u79fb\u540e\u7684 \\(h(x) = f(x+c) = \\displaystyle\\sum\\limits_{k=0}^K a_k\\left(x+c\\right)^k\\)\uff0c\u5176\u4e2d \\(c=-L+1\\) \u3002<\/p>\n<p>\u6839\u636e\u4e8c\u9879\u5f0f\u5b9a\u7406\u5c55\u5f00\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{k = 0}^K {{a_k}} \\sum\\limits_{j = 0}^k {\\left( {\\begin{array}{*{20}{c}} {k}\\\\ j \\end{array}} \\right) {x^j}{c^{k &#8211; j}}}\\) \u3002<\/p>\n<p>\u4ea4\u6362\u6c42\u548c\u6b21\u5e8f\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{j = 0}^K {{x^j}\\sum\\limits_{k = j}^K {{a_k} \\left( {\\begin{array}{*{20}{c}} {k}\\\\ j \\end{array}} \\right) } } {c^{k &#8211; j}}\\) \u3002<\/p>\n<p>\u8fd9\u6837 \\(h(x)\\) \u5c31\u53ef\u4ee5\u5728 \\(O(K^2)\\) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u6c42\u51fa\u6765\u4e86\u3002<\/p>\n<p>\u7ee7\u7eed\u5904\u7406\uff0c\u8bbe \\(t=k-j\\)\uff0c\u5219 \\(k=t+j\\)\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{j = 0}^K {{x^j}\\sum\\limits_{t = 0}^{K &#8211; j} {{a_{j+t}} \\left( {\\begin{array}{*{20}{c}} {j + t}\\\\ j \\end{array}} \\right)} } {c^t}\\) \u3002<\/p>\n<p>\u7ec4\u5408\u6570\u62c6\u5f00\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{j = 0}^K {\\frac{{{x^j}}}{{j!}}\\sum\\limits_{t = 0}^{K &#8211; j} {{a_{j + t}}\\left( {j + t} \\right)!} } \\frac{{{c^t}}}{{t!}}\\) \u3002<\/p>\n<p>\u5176\u5b9e\u5df2\u7ecf\u53ef\u4ee5\u770b\u51fa\u6765\u8fd9\u662f\u4e00\u4e2a<strong>\u5377\u79ef\u7684\u5f62\u5f0f<\/strong>\u4e86\u3002<\/p>\n<p>\u518d\u505a\u5904\u7406\uff0c\u8bbe \\(A_k = a_{K-k}\\left(K-k\\right)!\\)\uff0c\\(B_k = \\displaystyle\\frac{c^k}{k!}\\)\uff0c\u5219 \\(h(x) = \\displaystyle\\sum\\limits_{j = 0}^K {\\frac{{{x^j}}}{{j!}}\\sum\\limits_{t = 0}^{K &#8211; j} {{A_{K &#8211; j &#8211; t}}} {B_t}}\\) \u3002<\/p>\n<p>\u8bbe \\(g(n) = \\displaystyle\\sum\\limits_{t = 0}^n {{A_{n &#8211; t}}} {B_t}\\)\uff0c\u53ef\u4ee5\u7528 <strong>NTT<\/strong>\uff08\u4efb\u610f\u6a21\u6570FFT\uff09 \u5728 \\(O(K \\log K)\\) \u7684\u590d\u6742\u5ea6\u5185\u6c42\u51fa \\(n=0, 1, \\cdots, K\\) \u65f6\u51fd\u6570\u7684\u53d6\u503c\u3002<\/p>\n<p>\u6700\u540e \\(h(x) = \\displaystyle\\sum\\limits_{j = 0}^K {\\frac{{{x^j}}}{{j!}} g(K-j)}\\) \u5c31\u53ef\u4ee5\u5f97\u5230 \\(h(x)\\) \u7684\u5404\u9879\u7cfb\u6570\u4e86\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u4f46\u662f\u4e0a\u9762\u7684\u65b9\u6cd5\u4ec5\u9002\u7528\u4e8e<strong>\u5355\u70b9\u67e5\u8be2<\/strong>\uff0c<strong>\u533a\u95f4\u67e5\u8be2<\/strong>\u600e\u4e48\u529e\uff1f<\/p>\n<p>\u53d1\u73b0\u6bcf\u6b21\u8be2\u95ee\u4e00\u4e2a\u70b9\u5fc5\u987b\u8981 \\(O(\\max\\{K\\} \\log n)\\) \u7684\u590d\u6742\u5ea6\uff0c\u7531\u4e8e\u628a \\(c_i\\) \u770b\u6210\u662f\u591a\u9879\u5f0f\u7684\u5355\u70b9\u503c\u8fd9\u4e2a\u8bbe\u5b9a\uff0c\u6240\u4ee5\u5f88\u96be\u5728\u6570\u636e\u7ed3\u6784\u7b49\u65b9\u9762\u6709\u5176\u4ed6\u7684\u7a81\u7834\u3002<\/p>\n<p>\u6240\u4ee5\u53ef\u4ee5\u8003\u8651\u5728\u591a\u9879\u5f0f\u7b49\u65b9\u9762\u505a\u4e9b\u5904\u7406\u3002<\/p>\n<p>\u53ea\u652f\u6301\u5355\u70b9\u67e5\u8be2\uff0c\u53c8\u8981\u6c42\u533a\u95f4\u548c\uff0c\u6240\u4ee5\u53ef\u4ee5\u60f3\u5230\u7ef4\u62a4 \\(c\\) \u7684<strong>\u524d\u7f00\u548c<\/strong>\u3002<\/p>\n<p>\u8fd9\u6837\u52a0\u5165\u4e00\u4e2a\u591a\u9879\u5f0f \\(f(x)\\)\uff0c\u5c31\u76f8\u5f53\u4e8e\u5728 \\([L, R]\\) \u533a\u95f4\u52a0\u5b83\u7684<strong>\u524d\u7f00\u591a\u9879\u5f0f<\/strong> \\(h(x)\\)\uff0c\u5728 \\((R, N]\\) \u533a\u95f4\u52a0<strong>\u5e38\u6570 \\(h(R)\\)<\/strong> \u3002<\/p>\n<p>\u533a\u95f4\u67e5\u8be2\u65f6\u53ea\u9700\u67e5\u8be2 \\(c_R\\) \u548c \\(c_{L-1}\\) \u4e24\u5355\u70b9\u503c\u5373\u53ef\u3002<\/p>\n<p>\u524d\u7f00\u591a\u9879\u5f0f \\(h(x) = \\displaystyle\\sum\\limits_{j=1}^x f(j)\\)\uff0c\u5373 \\(h(x) = \\displaystyle\\sum\\limits_{j=1}^x \\sum\\limits_{k=0}^K a_kj^k\\)\u3002<\/p>\n<p>\u5c55\u5f00\uff0c\u6709 \\(h(x) = \\cdots\\cdots\\cdots\\) \u3002<\/p>\n<p>\u7b49\u7b49\uff0c\u8fd9\u600e\u4e48\u5c55\u5f00\uff1f\uff1f\uff1f\u91cc\u9762\u597d\u50cf\u6709\u7c7b\u4f3c\u4e8e \\(j^k\\) \uff08<strong>\u81ea\u7136\u6570\u5e42\u548c<\/strong>\uff09\u7684\u4e1c\u897f\uff0c\u8fd9\u600e\u4e48\u641e\uff1f<\/p>\n<p>\u8fd9\u91cc\u9009\u7528<strong>\u4f2f\u52aa\u5229\u516c\u5f0f<\/strong>\uff1a\\(\\displaystyle\\sum\\limits_{k=1}^x k^n = 1^n+2^n+\\cdots+x^n = \\frac{1}{{n + 1}}\\mathop \\sum \\limits_{k = 0}^n \\left( {\\begin{array}{*{20}{c}} {n + 1}\\\\ k \\end{array}} \\right)B_k^ + {x^{n + 1 &#8211; k}}\\) \u3002<\/p>\n<p>\u5176\u4e2d \\(B_k^+\\) \u4e3a<strong>\u4f2f\u52aa\u5229\u6570<\/strong>\u7684\u7b2c \\(k\\) \u9879\uff0c\\(\\displaystyle B_0=1,B_1^\\pm=\\pm\\frac{1}{2},B_2=\\frac{1}{6},B_3=0,B_4=\\frac{1}{30},\\cdots\\) \u3002<\/p>\n<p>\u4f2f\u52aa\u5229\u6570\u7684\u5b9a\u4e49\u5f0f\u4e3a \\({B_0} = 1\\)\uff0c\\(\\displaystyle\\sum\\limits_{i = 0}^n {B_i} \\left( {\\begin{array}{*{20}{c}} {n + 1}\\\\ i \\end{array}} \\right) = 0\\) \u3002<\/p>\n<p>\u6240\u4ee5\u53ef\u4ee5\u5f97\u5230\u5176\u9012\u63a8\u5f0f\u4e3a \\(B_0 = 1\\)\uff0c\\(B_n =\u00a0 -\\displaystyle\\frac{1}{{n + 1}}\\sum\\limits_{i = 0}^{n &#8211; 1} {\\left( {\\begin{array}{*{20}{c}} {n + 1}\\\\ i \\end{array}} \\right){B_i}} \\) \uff0c\u53ef\u4ee5\u5728 \\(O(K^2)\\) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u7b97\u51fa\u6765\uff0c\u6216\u6253\u8868 \\(O(1)\\)\uff0c\u6216\u591a\u9879\u5f0f\u6c42\u9006 \\(O(K \\log K)\\)\u3002<\/p>\n<p>\u7136\u540e\u5c31\u53ef\u4ee5\u7ee7\u7eed\u63a8 \\(h(x)\\) \u4e86\u3002<\/p>\n<p>\u4ea4\u6362\u6c42\u548c\u987a\u5e8f\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{k = 0}^K {{a_k}} \\sum\\limits_{j = 1}^x {{j^k}} \\) \u3002<\/p>\n<p>\u5e94\u7528\u4e0a\u9762\u7684\u516c\u5f0f\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{k = 0}^K {{a_k}\\frac{1}{{k + 1}}\\sum\\limits_{j = 0}^k {\\left( {\\begin{array}{*{20}{c}} {k + 1}\\\\ j \\end{array}} \\right)} B_j^ + {x^{k + 1 &#8211; j}}} \\) \u3002<\/p>\n<p>\u6362\u5143\uff0c\u8bbe \\(t=k-j\\)\uff0c\u5219 \\(j=k-t\\)\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{k = 0}^K {{a_k}\\frac{1}{{k + 1}}\\sum\\limits_{t = 0}^k {\\left( {\\begin{array}{*{20}{c}} {k + 1}\\\\ {k &#8211; t} \\end{array}} \\right)} B_{k &#8211; t}^ + {x^{t + 1}}} \\) \u3002<\/p>\n<p>\u518d\u6b21\u4ea4\u6362\u6c42\u548c\u987a\u5e8f\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{t = 0}^K {{x^{t + 1}}\\sum\\limits_{k = t}^K {\\frac{{{a_k}}}{{k + 1}}\\left( {\\begin{array}{*{20}{c}} {k + 1}\\\\ {k &#8211; t} \\end{array}} \\right)} B_{k &#8211; t}^ + } \\) \u3002<\/p>\n<p>\u8fd9\u6837 \\(h(x)\\) \u5c31\u53ef\u4ee5\u5728 \\(O(K^2)\\) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u6c42\u51fa\u6765\u4e86\u3002<\/p>\n<p>\u7ec4\u5408\u6570\u5c55\u5f00\uff0c\u518d\u6574\u7406\uff0c\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{t = 0}^K {\\frac{{{x^{t + 1}}}}{{(t + 1)!}}\\sum\\limits_{k = t}^K {{a_k}k!\\frac{{B_{k &#8211; t}^ + }}{{\\left( {k &#8211; t} \\right)!}}} } \\) \u3002<\/p>\n<p>\u662f\u4e0d\u662f\u5f88\u719f\u6089\uff1f\u518d\u6362\u5143\uff0c\u8bbe \\(j=k-t\\)\uff0c\u5219\u6709 \\(h(x) = \\displaystyle\\sum\\limits_{t = 0}^K {\\frac{{{x^{t + 1}}}}{{(t + 1)!}}\\sum\\limits_{j = 0}^{K &#8211; t} {{a_{j + t}}\\left( {j + t} \\right)!\\frac{{B_j^ + }}{{j!}}} } \\) \u3002<\/p>\n<p>\u662f\u4e0d\u662f\u66f4\u719f\u6089\u4e86\uff1f\u8bbe \\(A_k = a_{K-k}\\left(K-k\\right)!\\)\uff0c\\(C_k = \\displaystyle\\frac{{B_j^ + }}{{j!}}\\)\uff0c\u5219 \\(h(x) = \\displaystyle\\sum\\limits_{t = 0}^K {\\frac{{{x^{t + 1}}}}{{(t + 1)!}}\u00a0\\sum\\limits_{j = 0}^{K &#8211; t} A_{K-t-j}C_j }\\) \u3002<\/p>\n<p>\u8bbe \\(g(n) = \\displaystyle\\sum\\limits_{j = 0}^n {{A_{n &#8211; j}}} {C_j}\\)\uff0c\u53ef\u4ee5\u7528 <strong>NTT<\/strong>\uff08\u4efb\u610f\u6a21\u6570FFT\uff09 \u5728 \\(O(K \\log K)\\) \u7684\u590d\u6742\u5ea6\u5185\u6c42\u51fa \\(n=0, 1, \\cdots, K\\) \u65f6\u51fd\u6570\u7684\u53d6\u503c\u3002<\/p>\n<p>\u6700\u540e \\(h(x) = \\displaystyle\\sum\\limits_{t = 0}^K {\\frac{{{x^{t + 1}}}}{{(t + 1)!}} g(K-t)}\\) \u5c31\u53ef\u4ee5\u5f97\u5230 \\(h(x)\\) \u7684\u5404\u9879\u7cfb\u6570\u4e86\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u603b\u7ed3\u7684\u4e1c\u897f<\/p>\n<p>\u533a\u95f4\u52a0\u591a\u9879\u5f0f\uff08\u57fa\u672c\u533a\u95f4\u64cd\u4f5c\uff09\uff1a\u7ebf\u6bb5\u6811\uff1b\uff08\u6807\u8bb0\u6c38\u4e45\u5316\u6bd4\u6253 \\(tag\\) \u65f6\u95f4\u548c\u7a7a\u95f4\u90fd\u5c0f\u4e86\u4e00\u534a\u4ee5\u4e0a\uff09<\/p>\n<p>\u591a\u9879\u5f0f\u5e73\u79fb\uff08\u652f\u6301\u4efb\u610f\u533a\u95f4\u4fee\u6539\uff09\uff1aFFT\uff1b<\/p>\n<p>\u591a\u9879\u5f0f\u524d\u7f00\u548c\uff08\u652f\u6301\u533a\u95f4\u67e5\u8be2\uff09\uff1aFFT\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u6240\u4ee5\u672c\u9898\u672c\u6765\u5e94\u8be5\u662f FFT+FFT+\u7ebf\u00a0\u6bb5\u6811\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(QK \\log N + QK \\log K)\\)\uff0c\u5e38\u6570\u5de8\u5927\u3002<\/p>\n<p>\u7531\u4e8e\u540e\u9762 \\(Q\\) \u5f88\u5c0f\uff0c\u6240\u4ee5\u76f4\u63a5\u66b4\u529b\u662f\u80fd\u8dd1\u8fc7\u7684\uff0c\u7136\u540e\u4f60\u5c31\u53ef\u4ee5 * \u6807\u7b97\u4e86\uff09<\/p>\n<p>&nbsp;<\/p>\n<pre class=\"lang:default decode:true \">#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n\r\n#define _max(_a_,_b_) ((_a_)&gt;(_b_)?(_a_):(_b_))\r\n\r\n#define MOD 998244353\r\ntypedef long long LLONG;\r\n\r\n#ifdef ONLINE_JUDGE\r\n\tchar __B[1&lt;&lt;15],*__S=__B,*__T=__B;\r\n\t#define getchar() (__S==__T&amp;&amp;(__T=(__S=__B)+fread(__B,1,1&lt;&lt;15,stdin),__S==__T)?EOF:*__S++)\r\n#endif\r\n\r\ntemplate&lt;typename T&gt;\r\ninline T getnum()\r\n{\r\n\tregister char c=0;\r\n\tregister bool neg=false;\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar(),neg|=(c=='-');\r\n\tregister T a=0;\r\n\twhile(c&gt;='0' &amp;&amp; c&lt;='9')\r\n\t\ta=a*10+c-'0',c=getchar();\r\n\treturn (neg?-1:1)*a;\r\n}\r\n\r\ninline int _pow(register int base,register int b)\r\n{\r\n\tregister int ans=1;\r\n\twhile(b)\r\n\t{\r\n\t\tif(b&amp;1)\r\n\t\t\tans=(LLONG)ans*base%MOD;\r\n\t\tbase=(LLONG)base*base%MOD;\r\n\t\tb&gt;&gt;=1;\r\n\t}\r\n\treturn ans;\r\n}\r\n\r\n#define _KLIM 5005\r\nint as[_KLIM&lt;&lt;2],ck[_KLIM&lt;&lt;2],bk[_KLIM&lt;&lt;2];\r\n\r\nint flip[_KLIM&lt;&lt;2];\r\ninline void FFT(register int len,int c[],bool inverse=false)\r\n{\r\n\tregister int t=0;\r\n\tfor(register int i=0;i&lt;len;i++)\r\n\t\tif(i&lt;flip[i])\r\n\t\t\tt=c[flip[i]],c[flip[i]]=c[i],c[i]=t;\r\n\tfor(register int step=2;step&lt;=len;step&lt;&lt;=1)\r\n\t{\r\n\t\tregister int wn=_pow(3,(MOD-1)\/step);\r\n\t\tif(inverse)\r\n\t\t\twn=_pow(wn,MOD-2);\r\n\t\tregister int hstep=step&gt;&gt;1;\r\n\t\tstatic int pw[_KLIM&lt;&lt;2];\r\n\t\tpw[0]=1;\r\n\t\tfor(register int k=1;k&lt;=hstep;k++)\r\n\t\t\tpw[k]=(LLONG)pw[k-1]*wn%MOD;\r\n\t\tfor(register int k=0;k&lt;len;k+=step)\r\n\t\t\tfor(register int i=k;i &lt; k+hstep;i++)\r\n\t\t\t{\r\n\t\t\t\tregister int j=i+hstep;\r\n\t\t\t\tt=(LLONG)c[j]*pw[i-k]%MOD;\r\n\t\t\t\t(c[j]=c[i]-t)&lt;0 ? c[j]+=MOD : 0;\r\n\t\t\t\t(c[i]+=t)&gt;= MOD ? c[i]-=MOD : 0;\r\n\t\t\t}\r\n\t}\r\n\tif(inverse &amp;&amp; (t=_pow(len,MOD-2)))\r\n\t\tfor(register int i=0;i&lt;len;i++)\r\n\t\t\tc[i]=(LLONG)c[i]*t%MOD;\r\n}\r\n\r\n#define _TSIZE 60505050\r\nLLONG N;\r\nint sa[_TSIZE],tag[_TSIZE];\r\nint cnt,lson[_TSIZE],rson[_TSIZE];\r\nstruct STree\r\n{\r\n\tint root;\r\n\r\n\tLLONG Qpos,_Qret;\r\n\tinline void _QueryTree(register int o,register LLONG l,register LLONG r)\r\n\t{\r\n\t\tif(!o)\r\n\t\t\treturn;\r\n\t\tif(l==r)\r\n\t\t{\r\n\t\t\t(_Qret+=sa[o])%=MOD;\r\n\t\t\treturn;\r\n\t\t}\r\n\t\tregister LLONG mid=(l+r)&gt;&gt;1;\r\n\t\tif(Qpos&lt;=mid)\r\n\t\t\t_QueryTree(lson[o],l,mid);\r\n\t\telse\r\n\t\t\t_QueryTree(rson[o],mid+1,r);\r\n\t\t(_Qret+=tag[o])%=MOD;\r\n\t}\r\n\t\r\n\tinline int QueryTree(register LLONG pos)\r\n\t{\r\n\t\tQpos=pos,_Qret=0,_QueryTree(root,1,N);\r\n\t\treturn _Qret;\r\n\t}\r\n\t\r\n\tLLONG ML,MR,MV;\r\n\tinline void _ModifyTree(int&amp;o,register LLONG l,register LLONG r)\r\n\t{\r\n\t\tif(!o)\r\n\t\t\to=++cnt;\r\n\t\tif(ML&lt;=l &amp;&amp; MR&gt;=r)\r\n\t\t{\r\n\t\t\t(tag[o]+=MV)%=MOD;\r\n\t\t\tsa[o]=(sa[o]+(LLONG)MV*(r-l+1))%MOD;\r\n\t\t\treturn;\r\n\t\t}\r\n\t\tregister LLONG mid=(l+r)&gt;&gt;1;\r\n\t\tif(ML&lt;=mid)\r\n\t\t\t_ModifyTree(lson[o],l,mid);\r\n\t\tif(MR&gt;mid)\r\n\t\t\t_ModifyTree(rson[o],mid+1,r);\r\n\t\tsa[o]=(sa[lson[o]]+sa[rson[o]]+(LLONG)(r-l+1)%MOD*MV)%MOD;\r\n\t}\r\n\t\r\n\tinline void ModifyTree(register LLONG l,register LLONG r,const int&amp;val)\r\n\t{\r\n\t\tML=l,MR=r,MV=val,_ModifyTree(root,1,N);\r\n\t}\r\n\t\r\n}tree[_KLIM+1];\r\n\r\nint a[_KLIM+1]\/*,b[_KLIM+1]*\/;\r\nint fac[_KLIM+1],invfac[_KLIM+1],inv[_KLIM+1];\r\n#define _comb(_a,_b) ((LLONG)fac[_a]*invfac[_b]%MOD*invfac[(_a)-(_b)]%MOD)\r\nconst int 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main()\r\n{\r\n\/\/freopen(\"test.in\",\"r\",stdin);\r\n\tinvfac[0]=fac[0]=fac[1]=1;\r\n\tfor(register int i=2;i&lt;=_KLIM;i++)\r\n\t\tfac[i]=(LLONG)fac[i-1]*i%MOD;\r\n\tinvfac[_KLIM]=_pow(fac[_KLIM],MOD-2);\r\n\tfor(register int i=_KLIM-1;i&gt;=1;i--)\r\n\t\tinvfac[i]=(LLONG)invfac[i+1]*(i+1)%MOD;\r\n\tinv[0]=inv[1]=1;\r\n\tfor(register int i=2;i&lt;=_KLIM;i++)\r\n\t\tinv[i]=(LLONG)(MOD-MOD\/i)*inv[MOD%i]%MOD;\r\n\t\r\n\t\/*b[0]=1;\r\n\tfor(register int i=1;i&lt;=_KLIM;i++)\r\n\t{\r\n\t\tfor(register int j=0;j&lt;=i-1;j++)\r\n\t\t\tb[i]=(b[i]+(LLONG)b[j]*_comb(i+1,j))%MOD;\r\n\t\tb[i]=(LLONG)b[i]*(MOD-inv[i+1])%MOD;\r\n\t}\r\n\tb[1]=499122177;\r\n\tfor(register int i=0;i&lt;=_KLIM;i++)\r\n\t\tb[i]=(LLONG)b[i]*invfac[i]%MOD;*\/\r\n\t\r\n\tN=getnum&lt;LLONG&gt;();\r\n\tregister int Q=getnum&lt;int&gt;();\r\n\t\r\n\tregister int MK=0;\r\n\tlong long lastans=0;\r\n\tfor(register int lp=1;lp&lt;=Q;lp++)\r\n\t{\r\n\t\tregister int opt=getnum&lt;int&gt;();\r\n\t\tif(opt==0)\r\n\t\t{\r\n\t\t\tregister LLONG L=getnum&lt;LLONG&gt;()^(lastans*lastans);\r\n\t\t\tregister LLONG R=getnum&lt;LLONG&gt;()^(lastans*lastans);\r\n\t\t\tregister int K=getnum&lt;int&gt;();\r\n\t\t\tMK=_max(MK,K+1);\r\n\t\t\tfor(register int i=0;i&lt;=K;i++)\r\n\t\t\t\ta[i]=((getnum&lt;int&gt;()^lastans)+MOD)%MOD;\r\n\t\t\t\r\n\t\t\tregister int len=1,dig=0;\r\n\t\t\twhile(len&lt;((K+2)&lt;&lt;1))\r\n\t\t\t\tlen&lt;&lt;=1,dig++;\r\n\t\t\tfor(register int i=0;i&lt;len;i++)\r\n\t\t\t\tflip[i]=(flip[i&gt;&gt;1]&gt;&gt;1)|((i&amp;1)&lt;&lt;(dig-1)),\r\n\t\t\t\tas[i]=bk[i]=ck[i]=0;\r\n\t\t\t\r\n\t\t\tfor(register int k=0;k&lt;=K;k++)\r\n\t\t\t\tas[k]=(LLONG)fac[K-k]*a[K-k]%MOD,\r\n\t\t\t\tbk[k]=b[k];\r\n\t\t\t\r\n\t\t\tFFT(len,as),FFT(len,bk);\r\n\t\t\tfor(register int i=0;i&lt;len;i++)\r\n\t\t\t\tbk[i]=(LLONG)as[i]*bk[i]%MOD;\r\n\t\t\tFFT(len,bk,true);\r\n\t\t\t\r\n\t\t\ta[0]=0;\r\n\t\t\tfor(register int k=0;k&lt;=K;k++)\r\n\t\t\t\ta[k+1]=(LLONG)bk[K-k]*invfac[k+1]%MOD;\r\n\t\t\t\r\n\t\t\tK++;\r\n\t\t\tfor(register int k=0;k&lt;=K;k++)\r\n\t\t\t\tas[k]=(LLONG)fac[K-k]*a[K-k]%MOD;\r\n\t\t\tfor(register int i=K+1;i&lt;len;i++)\r\n\t\t\t\tas[i]=0;\r\n\t\t\tck[0]=1;\r\n\t\t\tfor(register int k=1,c=(-L+1)%MOD;k&lt;=K;k++)\r\n\t\t\t\tck[k]=((LLONG)c*ck[k-1]%MOD+MOD)%MOD;\r\n\t\t\tfor(register int k=0;k&lt;=K;k++)\r\n\t\t\t\tck[k]=(LLONG)ck[k]*invfac[k]%MOD;\r\n\t\t\t\r\n\t\t\tFFT(len,as),FFT(len,ck);\r\n\t\t\tfor(register int i=0;i&lt;len;i++)\r\n\t\t\t\tck[i]=(LLONG)as[i]*ck[i]%MOD;\r\n\t\t\tFFT(len,ck,true);\r\n\t\t\t\r\n\t\t\tfor(register int k=0;k&lt;=K;k++)\r\n\t\t\t\tas[k]=(LLONG)ck[K-k]*invfac[k]%MOD;\r\n\t\t\tfor(register int i=0;i&lt;=K;i++)\r\n\t\t\t\ttree[i].ModifyTree(L,R,as[i]);\r\n\t\t\t\r\n\t\t\tregister LLONG xr=R%MOD,ansr=0;\r\n\t\t\tfor(register int k=0,pwr=1;k&lt;=K;k++,pwr=(LLONG)pwr*xr%MOD)\r\n\t\t\t\tansr=(ansr+(LLONG)as[k]*pwr)%MOD;\r\n\t\t\tif(R+1&lt;=N)\r\n\t\t\t\ttree[0].ModifyTree(R+1,N,(int)ansr);\r\n\t\t}\r\n\t\telse\r\n\t\t{\r\n\t\t\tregister LLONG L=getnum&lt;LLONG&gt;()^(lastans*lastans);\r\n\t\t\tregister LLONG R=getnum&lt;LLONG&gt;()^(lastans*lastans);\r\n\t\t\tregister LLONG xl=(L-1)%MOD,xr=R%MOD,ans=0;\r\n\t\t\tfor(register int k=0,pwl=1,pwr=1;k&lt;=MK;k++)\r\n\t\t\t\tans=(ans-(LLONG)tree[k].QueryTree(L-1)*pwl%MOD\r\n\t\t\t\t\t\t+(LLONG)tree[k].QueryTree(R)*pwr%MOD +MOD)%MOD,\r\n\t\t\t\tpwl=(LLONG)pwl*xl%MOD,pwr=(LLONG)pwr*xr%MOD;\r\n\t\t\tprintf(\"%lld\\n\",lastans=ans);\r\n\t\t\t\/\/lastans=0;\r\n\t\t}\r\n\t}\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P4611 \u533a\u95f4\u52a0\u591a\u9879\u5f0f\uff08YJC \u7684\u6570\u7ec4\/\u591a\u9879\u5f0f\uff1f\uff09 \u65f6\u95f4\u9650\u5236\uff1a4444MS \u00a0\u00a0\u00a0\u00a0 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