UVALive - 3722 找规律

题意:找规律

题解:找规律

结论是\(a^n(x-1)-\sum_{i=1}^{n-1}a^i \mod\ c\)

#include<iostream>

#include<algorithm>

#include<cstdio>

#include<cstring>

#include<cstdlib>

#include<cmath>

#include<string>

#include<vector>

#include<stack>

#include<queue>

#include<set>

#include<map>

#define rep(i,j,k) for(register int i=j;i<=k;i++)

#define rrep(i,j,k) for(register int i=j;i>=k;i--)

#define erep(i,u) for(register int i=head[u];~i;i=nxt[i])

#define iin(a) scanf("%d",&a)

#define lin(a) scanf("%lld",&a)

#define din(a) scanf("%lf",&a)

#define s0(a) scanf("%s",a)

#define s1(a) scanf("%s",a+1)

#define print(a) printf("%lld",(ll)a)

#define enter putchar('\n')

#define blank putchar(' ')

#define println(a) printf("%lld\n",(ll)a)

#define IOS ios::sync_with_stdio(0)

using namespace std;

const int maxn = 1e6+11;

const int oo = 0x3f3f3f3f;

const double eps = 1e-7;

typedef long long ll;

ll MOD = 1e9+7;

inline ll mod(ll a){return a%MOD;}

ll read(){

    ll x=0,f=1;register char ch=getchar();

    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}

    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}

    return x*f;

}

ll fpw(ll a,ll n){

	ll ans=1;

	while(n){

		if(n&1) ans=mod(ans*a);

		n>>=1;

		a=mod(a*a);

	}

	return ans;

}

int sum(int p,int n){

    if(n==0)return 1;

    if(n&1) return mod(mod(1+fpw(p,n+1>>1))*mod(sum(p,n-1>>1)));

    else return mod(mod(1+fpw(p,n>>1))*mod(sum(p,(n>>1)-1))+mod(fpw(p,n)));

}

int main(){

	ll x,a,n;

	while(cin>>x>>a>>n>>MOD){

		if(x==0&&a==0&&n==0&&MOD==0)break;

		cout<<mod(mod(mod(fpw(a,n)*(x-1))-sum(a,n-1)+MOD)+1+MOD)<<endl;

	}

	return 0;

}