uva11429(生成随机数 期望)

//
//  main.cpp
//  uva11429
//
//  Created by New_Life on 16/8/4.
//  Copyright © 2016年 chenhuan001. All rights reserved.
//

#include <iostream>
#include <math.h>
#include <string>
#include <stdio.h>
#include <algorithm>
using namespace std;

#define N 1010
#define eps 1e-12

long double g[N];

int main(int argc, const char * argv[]) {
    int r,n;
    while(scanf("%d%d",&r,&n) && !(r==0&&n==0))
    {
        for(int i=0;i<n;i++)
        {
            int a,b;
            scanf("%d%d",&a,&b);
            g[i] = (long double)a/b;
        }
        long double sum = 1.0;
        long double dr = 1;
        long double up = 0;
        long double ans = 1.0;
        long double preans;
        do
        {
            long double tmp=0;
            dr *= r;
            up *= r;
            for(int i=0;i<n;i++)
            {
                long long tmpi = (long long)(g[i]*dr+eps);
                g[i] -= (long double)tmpi/dr;
                up += tmpi;
            }
            
            preans = ans;
            ans += (dr-up)/dr;
            
            //ans += sum;
        }while(ans-preans>1e-10);
        printf("%.6Lf\n",ans);
    }
    return 0;
}
/*
 100 3
 1 3 1 3 1 3
 2 4
 1 4 1 4 1 4 1 4
 2 3
 1 3 1 3 1 3
 10 2
 1 2 1 2
 */