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.Linq;
using System.Collections.Generic;
class c
{
    static void Main()
    {
        var nm = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        long ans = 1;
        var list = new List<long>();
        for (int i = 1; i <= Math.Sqrt(nm[1]); i++)
        {
            if (nm[1] % i == 0) list.Add(i);
        }
        for (int i = 0; i < list.Count(); i++)
        {
            if (nm[1] % list[i] == 0 && list[i] * nm[0] <= nm[1]) ans = Math.Max(ans, list[i]);
            if (nm[1] % (nm[1] / list[i]) == 0 && (nm[1] / list[i]) * nm[0] <= nm[1]) ans = Math.Max(ans, nm[1] / list[i]);
        }
        Console.WriteLine(ans);
    }
}