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;

namespace abc112_d
{
	class Program
	{
		static void Main(string[] args)
		{
			int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int max = x[1] / x[0];
			int ret = 1;
			for (int i = 1; i * i <= x[1]; i++)
			{
				if (x[1] % i == 0)
				{
					if (i <= max) ret = Math.Max(ret, i);
					if ((x[1] / i) <= max) ret = Math.Max(ret, x[1] / i);
				}
			}
			Console.WriteLine(ret);
		}
	}
}