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.Collections.Generic;
using System.Linq;

namespace ABC112_D
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var N = NM[0];
            var M = NM[1];

            var dM = Calcdivisors(M);
            long a = 0;

            foreach (var d in dM)
            {
                if (M / d >= N && d > a) a = d; 
            }
            Console.WriteLine(a);
        }

        public static List<long> Calcdivisors(long n)
        {
            var factors = new List<long>();

            for (long i = 1; i * i <= n; i ++)
            {
                if (n % i != 0) continue;
                factors.Add(i);
                if (n / i == i) continue;
                factors.Add(n / i);
            }
            return factors;
        }
    }
}