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.Generic;
using System.Linq;

class Program
{     
    public Program()
    {
      int[] inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
      int n = inputs[0];
      int m = inputs[1];
      int result = 
        Enumerable.Range(1, (int)Math.Sqrt(m) + 1)
        .Where(x => m % x == 0)
        .SelectMany(x => new int[]{x, m / x })
        .Where(x => x <= m / n)
        .Max();
      Console.WriteLine(result);
    }
    static void Main(string[] args)
    {
        var p = new Program();
    }
}