# "Lucas theorem/Fermat theorem/Chinese remainder theorem/extended Euclid" [Bzoj 1951] Ancient pig text

Source: Internet
Author: User
Tags mul

[Description] Ask

[Solution]
Easy to get,

So, the focus is on how to ask

If P-1 is a prime number, we can enumerate all d with the time of sqrt (n) and calculate the sum by the Lucas theorem respectively.
But we find that p-1=2*3*4679*35617 is not a prime number, so does Lucas ' theorem work? No, we can work out the model of 2, 3, 4679, 35617, and write four congruence equations, then solve them with grandson's theorem. Pay attention to the situation of special g==p, at this time Fermat theorem is not established, ans=0.

[Code]

``#include <cmath>#include <cstdio>typedef Long LONG Ll;constintMod=999911659; ll prime[4]={2,3,4679,35617};ll num[4],inver[4];void EXGCD (LLx, LLy, ll&a,ll&b) {if(!y) a=1, b=0;Else{EXGCD (y,x%y, b,a); B-=a*(x/y); }}ll Pow (ll a,ll N,intP) {ll ans=1; while(n) {if(n&1) Ans=ans*a%p; A=a*a%p; n>>=1; }returnAns;} ll C (LLm, ll N,ll p) {if(m<n)return 0;if(m==n)return 1;if(n>m-N) n=m-N; ll ans=1, cm=1, cn=1; for(LL i=0; i<n;i++) cm=cm*(m-I.)%p, CN=CN*(N-i)%p;returnCm*pow(cn,p-2, p)%p;} ll Lucas (LLm, ll N,ll p) {if(!n)return 1;return(Lucas (m/p,n/p, p)*c(m%pN%p, p))%p;}intGetintN) { for(intI=1, lim=sqrt(n) +1; i<lim;i++)if(! (n%i)){ for(intj=0;j<4; j + +) num[j]= (Num[j]+lucas (N,i,prime[j]))%prime[j];if(I*i-N) for(intj=0;j<4; j + +) num[j]= (Num[j]+lucas (N,n/i,prime[j]))%prime[j]; } ll Mul=1, ans=0; for(intI=0;i<4; i++) Mul*=Prime[i]; for(LL i=0,t;i<4; i++) {EXGCD (mul/prime[i],prime[i],inver[i],t); Inver[i]*=Mul/prime[i]; } for(intI=0;i<4; i++) ans= (Ans+num[i]*inver[i])%(mod-1);return(Ans+ (mod-1))%(mod-1);}intMain () {intN,g; scanf"%d%d", &n,&g);if(mod==g) {printf("0");return 0; } g%=MoDprintf("%lld", Pow (G,get (n), MoD));return 0;}``

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"Lucas theorem/Fermat theorem/Chinese remainder theorem/extended Euclid" [Bzoj 1951] Ancient pig text

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