Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.IO;
using System.Linq;
using System.Diagnostics;
using System.Globalization;
using static System.Console;
using static System.Math;

namespace abc112_d
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] input = ReadLine().Split().Select(int.Parse).ToArray();
            int n = input[0];
            int m = input[1];

            int ans = 1;
            for (int i = 1; i*i <= m; i++)
            {
                if(m % i == 0){
                    int x = m / i;
                    if((long)i*n <= m) ans = Max(ans, i);
                    if((long)x*n <= m) ans = Max(ans, x);
                }
            }
            WriteLine(ans);
        }
    }
}