Super a^b mod C fast Power + Euler function power down

uper a^b MoD CTime limit:1000MS Memory Limit:32768KB 64bit IO Format:%i64d &%i64 U SubmitStatus

Description

Given A,b,c, you should quickly calculate the result of A^b mod C. (1<=a,c<=1000000000,1<=b<=10^1000000).

Input

There is multiply testcases. Each testcase, there are one line contains three integers A, B and C, separated by A single space.

Output

For each testcase, output an integer, denotes the result of A^b mod C.

Sample Input

3 2 42) 10 1000

Sample Output

124 first to power down, from the power-down formula: (However, do not know how the formula came ...) Calculation of power after power-down

1#include <iostream>2#include <cstdio>3#include <algorithm>4#include <cstring>5#include <cmath>6 #definell __int647 #defineN 10001008 using namespacestd;9 CharB[n];Ten ll P[n]; One ll A, C; All Quick (ll A, ll b) {//Fast Power -ll k =1; -      while(b) { the         if(b%2==1){ -K = k*A; -K%=C; -         } +A = a*a%C; -b/=2; +     } A     returnK; at } - voidPriem () { -Memset (P,0,sizeof(P)); - ll I, J; -p[1] =1; -      for(i=2; I&LT;=SQRT (N); i++){ in          for(j=2; j<=n/i; J + +) -P[I*J] =1; to     } + } -ll Ola (ll N) {//Euler functions the ll I, J, R, AA; *R =N; $AA =N;Panax Notoginseng      for(i=2; I&LT;=SQRT (n); i++){ -         if(!P[i]) { the             if(aa%i==0){ +R = r/i* (i-1); A                  while(aa%i==0) theAA/=i; +             } -         } $     } $     if(aa>1) -R = r/aa* (aa-1); -     returnR; the } - intMain () {Wuyi ll D, I, J; the Priem (); -      while(~SCANF ("%i64d%s%i64d",&a,b,&c)) { Wull L =strlen (b); -ll b=0; Aboutll OC =Ola (c); $       //cout<< "OC =" <<oc<<endl; -          for(i=0; i<l; i++){ -B = b*Ten+b[i]-'0'; -             if(b>oc) A                  Break; +         } the         //cout<<i<<endl; -         if(i==l) $D =Quick (A, b); the         Else{ theb=0; the              for(i=0; i<l; i++) {//Power down theB = (b*Ten+b[i]-'0')%OC; -             } inD = Quick (a,b+oc); the         } the       //printf ("b=%i64d\n", B); Aboutprintf"%i64d\n", d); the     } the     return 0; the}

Super a^b mod C fast Power + Euler function power down