{"id":53112,"date":"2025-08-12T00:29:33","date_gmt":"2025-08-11T16:29:33","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/53112.html"},"modified":"2025-08-12T00:29:33","modified_gmt":"2025-08-11T16:29:33","slug":"%e3%80%90c%e7%ab%9e%e8%b5%9b%e3%80%91%e5%8f%96%e6%a8%a1","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/53112.html","title":{"rendered":"\u3010C++\u7ade\u8d5b\u3011\u53d6\u6a21"},"content":{"rendered":"<h4>\u53d6\u6a21\u8fd0\u7b97\u7684\u610f\u4e49<\/h4>\n<p>\u53d6\u6a21\u8fd0\u7b97&#xff08;Modulo Operation&#xff09;\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u6570\u5b66\u4e2d\u5177\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u5176\u6838\u5fc3\u4f5c\u7528\u662f\u5c06\u6570\u503c\u9650\u5236\u5728\u7279\u5b9a\u8303\u56f4\u5185&#xff0c;\u907f\u514d\u6ea2\u51fa\u6216\u7b80\u5316\u95ee\u9898\u3002<\/p>\n<p>\u53d6\u6a21\u8fd0\u7b97\u901a\u5e38\u8868\u793a\u4e3a a % m&#xff0c;\u7ed3\u679c\u4e3a a \u9664\u4ee5 m \u7684\u4f59\u6570\u3002\u6570\u5b66\u4e0a\u5b9a\u4e49\u4e3a&#xff1a;<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[amod\u2009\u2009m&#061;a\u2212m\u22c5\u230aam\u230b][ a \\\\mod m &#061; a &#8211; m \\\\cdot \\\\left\\\\lfloor \\\\frac{a}{m} \\\\right\\\\rfloor ]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace allowbreak\"><\/span><span class=\"mspace\" style=\"margin-right: 0.6667em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4445em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2em;vertical-align: -0.35em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">\u230a<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6954em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">\u230b<\/span><\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53d6\u6a21\u8fd0\u7b97\u7684\u4e3b\u8981\u610f\u4e49\u5305\u62ec&#xff1a;<\/p>\n<ul>\n<li>\u9632\u6b62\u6570\u503c\u6ea2\u51fa&#xff1a;\u5728\u8ba1\u7b97\u673a\u4e2d&#xff0c;\u6570\u503c\u7c7b\u578b\u6709\u8303\u56f4\u9650\u5236&#xff0c;\u53d6\u6a21\u53ef\u5c06\u5927\u6570\u6620\u5c04\u5230\u6709\u9650\u8303\u56f4\u5185\u3002<\/li>\n<li>\u5faa\u73af\u6027\u8d28&#xff1a;\u53d6\u6a21\u8fd0\u7b97\u5177\u6709\u5468\u671f\u6027&#xff0c;\u9002\u5408\u5904\u7406\u5faa\u73af\u7ed3\u6784&#xff08;\u5982\u65f6\u95f4\u3001\u89d2\u5ea6&#xff09;\u3002<\/li>\n<li>\u5bc6\u7801\u5b66\u5e94\u7528&#xff1a;\u5728\u52a0\u5bc6\u7b97\u6cd5\u4e2d\u5e7f\u6cdb\u4f7f\u7528\u6a21\u8fd0\u7b97\u6765\u4fdd\u8bc1\u5b89\u5168\u6027\u3002<\/li>\n<li>\u7b97\u6cd5\u4f18\u5316&#xff1a;\u5728\u52a8\u6001\u89c4\u5212\u3001\u6570\u8bba\u95ee\u9898\u4e2d&#xff0c;\u53d6\u6a21\u53ef\u7b80\u5316\u8ba1\u7b97\u3002<\/li>\n<\/ul>\n<h4>\u6807\u51c6\u6a21\u6570 998244353<\/h4>\n<p>\u5728\u7b97\u6cd5\u7ade\u8d5b\u548c\u6570\u5b66\u95ee\u9898\u4e2d&#xff0c;998244353 \u662f\u4e00\u4e2a\u5e38\u7528\u7684\u6807\u51c6\u6a21\u6570&#xff0c;\u5176\u9009\u62e9\u57fa\u4e8e\u4ee5\u4e0b\u7279\u6027&#xff1a;<\/p>\n<li>\n<p>\u8d28\u6570\u6027\u8d28&#xff1a;<\/p>\n<ul>\n<li>998244353 \u662f\u4e00\u4e2a\u5927\u8d28\u6570&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(223\u00d7119&#043;1)(2^{23} \\\\times 119 &#043; 1)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">23<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">119<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u5176\u503c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(998244353)(998244353)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">998244353<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u8d28\u6570\u7684\u6027\u8d28\u4fdd\u8bc1\u4e86\u6a21\u8fd0\u7b97\u4e0b\u7684\u9664\u6cd5&#xff08;\u4e58\u6cd5\u9006\u5143&#xff09;\u5b58\u5728\u4e14\u552f\u4e00\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u539f\u6839\u5b58\u5728\u6027&#xff1a;<\/p>\n<ul>\n<li>\u8be5\u6a21\u6570\u7684\u6700\u5c0f\u539f\u6839\u4e3a 3&#xff0c;\u9002\u5408\u5feb\u901f\u6570\u8bba\u53d8\u6362&#xff08;NTT&#xff09;&#xff0c;\u7528\u4e8e\u9ad8\u6548\u8ba1\u7b97\u591a\u9879\u5f0f\u4e58\u6cd5\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6570\u503c\u8303\u56f4&#xff1a;<\/p>\n<ul>\n<li>\u4ecb\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(108)\u5230(109)(10^8) \u5230 (10^9)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord cjk_fallback\">\u5230<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4&#xff0c;\u9002\u5408 32 \u4f4d\u6574\u6570\u8fd0\u7b97&#xff0c;\u907f\u514d\u6ea2\u51fa\u3002<\/li>\n<li>\u5e73\u65b9\u4e0d\u8d85\u8fc7 64 \u4f4d\u6574\u6570\u8303\u56f4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">&#xff08;(9982443532&lt;263)&#xff09;&#xff08;(998244353^2 &lt; 2^{63})&#xff09;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord cjk_fallback\">&#xff08;<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">99824435<\/span><span class=\"mord\"><span class=\"mord\">3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">63<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord cjk_fallback\">&#xff09;<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u8ba1\u7b97\u6548\u7387&#xff1a;<\/p>\n<ul>\n<li>\u4e8c\u8fdb\u5236\u8868\u793a\u4e3a 11101110000000000001110000000001&#xff0c;\u4fbf\u4e8e\u4f4d\u8fd0\u7b97\u4f18\u5316\u3002<\/li>\n<li>\u6a21\u6570\u51cf\u4e00&#xff08;(998244352)&#xff09;\u7684\u8d28\u56e0\u6570\u5206\u89e3\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">(223\u00d7119)(2^{23} \\\\times 119)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">23<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">119<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u9002\u5408\u5206\u6cbb\u7b97\u6cd5\u3002<\/li>\n<\/ul>\n<\/li>\n<h4>\u53d6\u6a21\u8fd0\u7b97\u7684\u5b9e\u73b0<\/h4>\n<p>\u5728\u7f16\u7a0b\u4e2d&#xff0c;\u53d6\u6a21\u8fd0\u7b97\u9700\u6ce8\u610f\u8d1f\u6570\u5904\u7406\u3002\u4f8b\u5982\u5728 C&#043;&#043; \u4e2d&#xff1a;<\/p>\n<p><span class=\"token keyword\">const<\/span> <span class=\"token keyword\">int<\/span> MOD <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">998244353<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">mod<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> a<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token punctuation\">(<\/span>a <span class=\"token operator\">%<\/span> MOD <span class=\"token operator\">&#043;<\/span> MOD<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">%<\/span> MOD<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u5bf9\u4e8e\u4e58\u6cd5\u53d6\u6a21&#xff0c;\u9700\u9632\u6b62\u4e2d\u95f4\u7ed3\u679c\u6ea2\u51fa&#xff1a;<\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">mul_mod<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> a<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> b<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1LL<\/span> <span class=\"token operator\">*<\/span> a <span class=\"token operator\">*<\/span> b<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">%<\/span> MOD<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h4>\u9006\u5143\u8ba1\u7b97<\/h4>\n<p>\u5728\u6a21\u8fd0\u7b97\u4e2d&#xff0c;\u9664\u6cd5\u901a\u8fc7\u4e58\u6cd5\u9006\u5143\u5b9e\u73b0\u3002\u6839\u636e\u8d39\u9a6c\u5c0f\u5b9a\u7406&#xff0c;\u82e5 MOD \u4e3a\u8d28\u6570&#xff0c;\u5219\u9006\u5143\u4e3a&#xff1a;<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[a\u22121\u2261aMOD\u22122(modMOD)][ a^{-1} \\\\equiv a^{MOD-2} \\\\pmod{MOD} ]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2261<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8413em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">MO<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace allowbreak\"><\/span><span class=\"mspace\" style=\"margin-right: 0.4444em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.3333em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">MO<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mclose\">)]<\/span><\/span><\/span><\/span><\/span><br \/>\n\u4ee3\u7801\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">inv<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> a<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> res <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> p <span class=\"token operator\">&#061;<\/span> MOD <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>p <span class=\"token operator\">&amp;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> res <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">mul_mod<\/span><span class=\"token punctuation\">(<\/span>res<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        a <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">mul_mod<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        p <span class=\"token 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