ural 1110 Power



1110. Power

Time limit: 0.5 second

Memory limit: 64 MB

You are given the whole numbers N, M and
Y. Write a program that will find all whole numbers X in the interval [0,
M ? 1] such that X^N mod
M = Y.

Input

The input contains a single line with N,
M and Y (0 < N < 999, 1 < M < 999, 0 < Y < 999) separated with one space.

Output

Output all numbers X separated with space on one line. The numbers must be written in ascending order. If no such numbers exist then output ?1.

Sample

2 6 4

2 4

Problem Source: Bulgarian National Olympiad Day #1

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题意：是否存在x,使得x的n次方%m等于y，存在的话输出所有的x。不存在输出负一。

水题，跑个快速幂。

#include <cstdio>
#include <iostream>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
int m;
int fast_mi(int a,int k)
{
    int res=1;
    while(k)
    {
        if(k&1)
            res=res*a%m;
        a=a*a%m;
        k>>=1;
    }
    return res;
}
int main()
{
    int n,y,i;
    int a[1000];
    while(cin>>n>>m>>y)
    {
        int flag=0;
        memset(a,0,sizeof(a));
        int len=0;
        for(i=0; i<=m-1; i++)
        {
            if(fast_mi(i,n)%m==y)
            {
                flag=1;
                a[len++]=i;
            }
        }
        if(flag)
        {
            for(i=0; i<len; i++)
            {
                if(!i)
                    cout<<a[i];
                else
                    cout<<" "<<a[i];
            }
            cout<<endl;
        }
        else
            cout<<-1<<endl;
    }
    return 0;
}