\u6211\u4eec\u4e0d\u59a8\u5c06\u539f\u5f0f\u9012\u5f52\u5c55\u5f00\uff0c\u53ef\u4ee5\u5f97\u5230\u5f62\u5982\u6b64\u7684\u5f0f\u5b50\uff1a
\n$$f_{n}=a^nf_{0}+\\frac{(a^{n}-1)c}{a-1}$$
\n\u5bf9\u4e8e\u8fd9\u4e2a\u5f0f\u5b50\u7684\u503c\uff0c\u6211\u4eec\u770b\u4f3c\u53ef\u4ee5\u4e0a\u4e00\u4e2a\u5feb\u901f\u5e42\u76f4\u63a5\u6c42\u5f97\u3002
\n\u7136\u800c\u4ed4\u7ec6\u89c2\u5bdf\u4e0a\u5f0f\u7684\u60c5\u51b5\uff0c\u53d1\u73b0\u5982\u679c\u51fa\u73b0\u4e86\u5947\u5999\u7684\u6a21\u6570\u65f6\uff0c\\(a-1\\)\u662f\u4e0d\u4e00\u5b9a\u6709\u9006\u5143\u7684\uff01
\n\u8fd9\u5c31\u5f88\u4ee4\u4eba\u96be\u53d7\u4e86\u3002
\n\u6211\u4eec\u627e\u5230\u539f\u6765\u7684\u95ee\u9898\uff0c\u6211\u4eec\u4e0d\u5f97\u4e0d\u6c42\u4e0b\u8ff0\u5f0f\u5b50\u7684\u503c\uff1a
\n$$f_{n}=a^nf_{0}+\\sum_{i=0}^{n-1}a^ic=a^nf_{0}+(\\sum_{i=0}^{n-1}a^i)c$$
\n\u6c42\u503c\u7684\u6700\u5927\u969c\u788d\u662f\u8fd9\u4e2a\u5f0f\u5b50\uff1a
\n$$\\sum_{i=0}^{n-1}a^i$$
\n\u5c06\u8fd9\u4e2a\u5f0f\u5b50\u5206\u5947\u5076\u8ba8\u8bba\u540e\u9012\u5f52\u6c42\u89e3\u3002
\n\u6211\u4eec\u4ee4\uff1a
\n$$u_{x}=\\sum_{i=0}^{x-1}a^i$$
\n\u82e5\u662f\u5076\u6570\uff0c\u5219\u6709\uff1a
\n$$u_x=\\sum_{i=0}^{\\frac{x-1}{2}}a^i+a^{\\frac{x+1}{2}} (\\sum_{i=0}^{\\frac{x-1}{2}}a^i)$$
\n\u5373\uff0c
\n$$u_x=(a^{\\frac{x+1}{2}}+1)u_{\\frac{x-1}{2}}$$
\n\u82e5\u662f\u5947\u6570\uff0c\u5219\u53ea\u9700\u5c06\u7b2c\u4e00\u9879\u5355\u72ec\u8ba1\u7b97\u3002
\n\u8fd9\u6837\u5c31\u53ef\u4ee5\u5728\u5bf9\u6570\u590d\u6742\u5ea6\u5185\u5bf9\u5f0f\u5b50\u6c42\u89e3\u4e86\u3002
\n\u53e6\u5916\uff0c\u8003\u8651\u5230\u6a21\u6570\u7684\u6570\u636e\u8303\u56f4\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u4e00\u79cd\u88ab\u79f0\u4e3a\u300c\u9f9f\u901f\u4e58\u300d\uff0c\u4e5f\u5c31\u662f\u300c\u5feb\u901f\u5e42\u300d\u5728\u4e58\u6cd5\u610f\u4e49\u4e0a\u7684\u7b49\u540c\u7684\u64cd\u4f5c\uff0c\u4f7f\u5f97\u4e0d\u4f1a\u51fa\u73b0\u4e58\u6cd5\uff0c\u4e5f\u5c31\u4e0d\u4f1a\u7206\u8303\u56f4\u3002<\/p>\n\n\n\n
#include<iostream>\n#include<cstdio>\n\nlong long MOD,a,c,x0,n,g;\n\/\/\u5fc5\u987b\u6ce8\u610f\uff0c\u4e0d\u80fd\u91cd\u8f7d\u4e00\u4e2a\u5168\u90e8\u662f\u6807\u51c6\u578b\u7684\u8fd0\u7b97\u7b26\u3002 \ninline long long mlt(long long A,long long X){\n\tlong long BS=A,RT=0,CNT=X;\n\twhile(CNT){\n\t\tif(CNT&1){\n\t\t\tRT+=BS;\n\t\t\tRT%=MOD;\n\t\t}\n\t\tCNT>>=1;\n\t\tBS+=BS;\n\t\tBS%=MOD;\n\t}\n\treturn RT;\n}\ninline long long pw(long long A,long long X){\n\tlong long BS=A,RT=1,CNT=X;\n\twhile(CNT){\n\t\tif(CNT&1){\n\t\t\tRT=mlt(RT,BS)%MOD;\n\t\t}\n\t\tCNT>>=1;\n\t\tBS=mlt(BS,BS)%MOD;\n\t}\n\treturn RT;\n}\ninline long long calc(long long X){\n\tif(X==2){\n\t\treturn (a+1)%MOD;\n\t}\n\tif(X==1){\n\t\treturn 1;\n\t}\n\tif(X&1){\n\t\treturn (pw(a,X-1)+calc(X-1))%MOD;\n\t}\n\treturn mlt((pw(a,(X+1)>>1)+1),calc(X>>1));\n}\nvoid init(){\n\tscanf(\"%lld%lld%lld%lld%lld%lld\",&MOD,&a,&c,&x0,&n,&g);\n\tprintf(\"%lld\",((mlt(pw(a,n),x0)+mlt(calc(n),c))%MOD)%g);\n}\n\nint main(){\n\tinit();\n\treturn 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"\u6211\u4eec\u4e0d\u59a8\u5c06\u539f\u5f0f\u9012\u5f52\u5c55\u5f00\uff0c\u53ef\u4ee5\u5f97\u5230\u5f62\u5982\u6b64\u7684\u5f0f\u5b50\uff1a $$f_{n}=a^nf_{0}+\\frac{(a^{n}-1 … <\/p>\n