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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = l[0], M = l[1];

            if (M % N == 0)
                Console.WriteLine(M / N);
            else
            {
                var div = M / N;
                var rem = M % N;
                var max = Gcd(div, rem);

                while (N > 1)
                {
                    N--;
                    div = M / N;
                    rem = M % N;
                    if (M % N == 0) continue;
                    max = Math.Max(max, Gcd(div, rem));
                }

                Console.WriteLine(max);
            }
        }

        static int Gcd(int a, int b)
        {
            if (a < b) Gcd(b, a);
            if (b == 0) return a;
            return Gcd(b, (a % b));
        }
    }
}