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 Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            // 写経
            var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var ans = 1L;

            for (var a = 1L; a * a <= nm[1]; a++)
            {
                if (nm[1] % a != 0) continue;

                var b = nm[1] / a;

                if (a * nm[0] <= nm[1]) ans = Math.Max(ans, a);
                if (b * nm[0] <= nm[1]) ans = Math.Max(ans, b);
            }

            Console.WriteLine(ans);
        }
    }
}