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 Program
{
    /**
    * a1 + a2 + a3 + ... + aN = M
    * D*1 + D*1 + D*1 + ... + D*1 = ND
    * したがって、M >= ND
    * また、約数の性質として√M以下のがペアのひとつになる。
    * ※M = a*b >= a*aより導かれる
    * M >= NDとなるものは任意に構成できるので
    * M / Nの最大値を考えればよい。
    */
    static void Main(string[] args)
    {
        var inputs = Console.ReadLine().Split(' ');
        var N = int.Parse(inputs[0]);
        var M = long.Parse(inputs[1]);

        var max = 1L;
        for (long A = 1; A * A <= M; A++)
        {
            if (M % A != 0) continue;

            // M = A * N;
            if (A * N <= M) max = Math.Max(A, max);

            long B = M / A;
            if (B * N <= M) max = Math.Max(B, max);

        }

        Console.WriteLine(max);
    }



}