https://cn.vjudge.net/problem/UVA-11582
要求斐波那契的第a^b项模n是多少 a和b都是ull的范围 但是n很小 极有可能存在循环节
暴力打表 果然n从1到1000的循环节都在1e3级别 pre[n]记为n对应的循环节 这样将a^b对pre[n]取模 然后暴力求第(a^b)%pre[n]项即可
#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
const int maxn=1e3+10;
ull pre[maxn]={0,1,3,8,6,20,24,16,12,24,60,10,24,28,48,40,24,36,24,18,60,16,30,48,24,100,84,72,48,14,120,30,48,40,36,80,24,76,18,56,60,40,48,88,30,120,48,32,24,112,300,72,84,108,72,20,48,72,42,58,120,60,30,48,96,140,120,136,36,48,240,70,24,148,228,200,18,80,168,78,120,216,120,168,48,180,264,56,60,44,120,112,48,120,96,180,48,196,336,120,300,50,72,208,84,80,108,72,72,108,60,152,48,76,72,240,42,168,174,144,120,110,60,40,30,500,48,256,192,88,420,130,120,144,408,360,36,276,48,46,240,32,210,140,24,140,444,112,228,148,600,50,36,72,240,60,168,316,78,216,240,48,216,328,120,40,168,336,48,364,180,72,264,348,168,400,120,232,132,178,120,90,336,120,48,380,120,180,96,144,180,190,96,388,588,280,336,396,120,22,300,136,150,112,72,40,624,48,168,90,240,42,108,280,72,440,72,240,108,296,60,252,456,448,48,600,228,456,72,114,240,80,84,52,168,160,174,312,144,238,120,240,330,648,60,560,120,252,60,168,1500,250,48,240,768,360,384,516,264,304,420,168,390,176,120,540,144,88,408,268,360,270,72,112,276,100,48,556,138,120,240,56,96,568,210,360,420,80,48,612,420,392,444,588,336,580,228,360,444,336,600,176,150,200,72,60,72,88,240,208,60,310,168,628,948,240,78,636,216,70,480,72,48,36,216,700,984,216,120,32,120,110,168,456,336,680,48,676,1092,152,180,30,72,784,264,240,348,232,168,174,1200,504,240,236,696,140,132,144,534,358,120,342,90,440,336,740,120,736,48,120,1140,432,120,748,180,1000,96,28,144,378,180,256,570,768,192,80,1164,264,588,388,840,144,336,520,396,780,120,796,66,144,600,200,408,420,150,1080,336,380,72,408,120,552,624,464,48,840,336,184,90,418,240,84,42,96,108,900,840,240,72,280,1320,430,72,868,240,280,108,144,888,438,60,336,252,888,456,220,1344,296,96,448,600,40,228,200,456,560,72,916,114,72,240,46,240,928,168,120,156,936,168,272,480,632,348,440,312,900,144,216,714,478,240,532,240,48,330,980,648,976,60,328,1680,490,120,252,252,120,120,560,168,498,1500,336,750,1008,48,100,240,728,768,254,360,592,768,72,516,1040,264,160,912,696,420,26,168,1048,390,400,528,180,120,1104,540,696,144,280,264,360,408,712,804,560,360,90,270,360,144,540,336,1096,276,120,300,126,48,624,1668,760,138,124,120,616,240,360,168,376,96,380,1704,432,420,568,360,570,420,760,240,1200,96,1156,612,776,420,336,1176,540,444,840,588,1176,336,90,1740,792,456,1188,360,720,444,88,336,598,600,600,528,408,150,220,600,1216,144,112,60,224,72,1228,264,40,240,1236,624,206,60,144,930,176,168,2500,1884,360,948,684,240,630,156,168,636,1280,216,112,210,840,960,640,72,1288,48,440,36,1296,216,290,2100,240,984,1308,216,260,120,888,96,658,120,220,330,504,168,720,456,336,336,448,2040,60,48,1348,2028,1800,1092,452,456,784,180,456,30,1368,72,1380,2352,456,264,756,240,138,348,240,696,460,168,360,174,104,1200,700,504,684,480,160,708,400,696,118,420,312,132,240,144,140,534,952,1074,718,120,208,342,240,90,700,1320,1456,336,1944,2220,792,120,1468,2208,560,48,680,120,738,1140,504,432,496,120,740,2244,168,180,144,3000,750,96,1000,84,100,144,1516,378,240,180,380,768,432,570,360,768,812,384,192,240,1032,1164,1548,264,300,588,304,1164,360,840,70,144,504,336,1580,1560,1576,396,176,780,304,120,420,2388,1080,66,228,144,288,1200,264,600,740,408,240,420,536,300,202,1080,270,336,1080,1140,1640,72,792,408,336,120,820,552,1648,624,200,1392,1656,48,276,840,1112,672,1008,552,1680,90,360,1254,838,240,406,84,56,42,1820,96,880,216,568,900,912,840,1708,240,360,72,1716,840,78,1320,80,1290,1728,144,1740,2604,1224,240,390,840,952,108,1176,144,2000,888,1756,438,1176,120,176,336,1768,252,1160,888,1776,456,256,660,1080,1344,288,888,1780,192,336,1344,210,600,108,120,176,228,180,600,1816,456,600,1680,70,72,840,2748,120,114,1040,72,102,240,88,138,140,240,1900,2784,624,336,928,120,1008,156,1240,936,180,168,1876,816,1256,480,470,1896,240,696,720,1320,1896,312,1036,900,1272,144,212,216,380,714,280,1434,1104,480,930,1596,72,240,1940,48,176,660,72,2940,970,648,368,2928,1400,120,652,984,220,1680,216,1470,1968,120,1980,252,32,252,528,120,198,240,440,1680,220,168,1996,498,1368,1500};
ull quickpow(ull a,ull b,ull mod)
{
ull res;
a%=mod;
res=1;
while(b>0){
if(b%2) res=(res*a)%mod;
a=(a*a)%mod,b/=2;
}
return res;
}
int main()
{
ull a,b,res;
int fib[10*maxn];
int t,n,i;
scanf("%d",&t);
while(t--){
scanf("%llu%llu%d",&a,&b,&n);
res=quickpow(a,b,pre[n]);
fib[0]=0,fib[1]=1%n;
for(i=2;i<=res;i++){
fib[i]=(fib[i-1]+fib[i-2])%n;
}
printf("%d\n",fib[res]);
}
return 0;
}