Time Limit:1000MS	Memory Limit:30000K
Total Submissions:8010	Accepted:4875

Description

People are different. Some secretly read magazines full of interesting girls' pictures, others create an A-bomb in their cellar, others like using Windows, and some like difficult mathematical games. Latest marketing research shows, that this market segment was so far underestimated and that there is lack of such games. This kind of game was thus included into the KOKODáKH. The rules follow:

Each player chooses two numbers Ai and Bi and writes them on a slip of paper. Others cannot see the numbers. In a given moment all players show their numbers to the others. The goal is to determine the sum of all expressions Ai^Bifrom all players including oneself and determine the remainder after division by a given number M. The winner is the one who first determines the correct result. According to the players' experience it is possible to increase the difficulty by choosing higher numbers.

You should write a program that calculates the result and is able to find out who won the game.

Input

The input consists of Z assignments. The number of them is given by the single positive integer Z appearing on the first line of input. Then the assignements follow. Each assignement begins with line containing an integer M (1 <= M <= 45000). The sum will be divided by this number. Next line contains number of players H (1 <= H <= 45000). Next exactly H lines follow. On each line, there are exactly two numbers Ai and Bi separated by space. Both numbers cannot be equal zero at the same time.

Output

For each assingnement there is the only one line of output. On this line, there is a number, the result of expression

(A₁^B₁+A₂^B₂+ ... +A_H^B_H)mod M.

Sample Input

3
16
4
2 3
3 4
4 5
5 6
36123
1
2374859 3029382
17
1
3 18132

Sample Output

2
13195
13

Source

問題簡述：參見上述連結。

問題分析：

這是一個單純的模冪計算和求和問題，呼叫模冪計算函式即可。

不用快速模冪計算的話，時間上會超時。

程式說明：函式powermod()是模冪計算函式。

AC的C++語言程式如下：

/* POJ1995 ZOJ2150 Raising Modulo Numbers */

#include <iostream>

using namespace std;

typedef unsigned long long ULL;

// 模冪計算
ULL powermod(ULL a, ULL n, ULL m)
{
    ULL res = 1LL;
    while(n) {
        if(n & 1LL) {        // n % 2 == 1
            res *= a;
            res %= m;
        }
        a *= a;
        a %= m;
        n >>= 1;
    }
    return res;
}

int main()
{
    int z, m, h, ai, bi, ans;

    cin >> z;
    while(z--) {
        cin >> m >> h;

        ans = 0;
        while(h--) {
            cin >> ai >> bi;

            ans += (int)powermod(ai, bi, m);
        }
        ans %= m;
        cout << ans << endl;
    }

    return 0;
}