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;

namespace ABC112
{
    class D
    {
        static void Main(string[] args)
        {
            long[] input = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long N = input[0];
            long M = input[1];

            long res = 0;

            for (long i = 1; i <= Math.Sqrt(M) + 1; i++)
            {

                if (M % i == 0)
                {
                    if (i <= M / N) res = Math.Max(res, i);
                    if (M / i <= M / N) res = Math.Max(res, M / i);
                }

            }
            Console.WriteLine(res);

        }
    }
}