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 CSharpSample01
{

    
    
    class Program
    {

        //約数を昇順リストで返す
        //O(√N)
        static List<int> Divisor(int M)
        {
            List<int> divlist = new List<int>();

            for(int i = 1; i * i <= M; i++)
            {
                if(M % i == 0)
                {
                    divlist.Add(i);
                    if (i * i != M) divlist.Add(M / i);
                }
            }

            divlist.Sort();

            return divlist;
        }

        static int Solve(int N, int M, List<int> divisor)
        {

            for(int i = divisor.Count - 1; i >= 0; i--)
            {
                if(N <= (M / divisor[i]))
                {
                    return divisor[i];
                }
            }

            return 1;
        }

        
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int M = int.Parse(input[1]);

            List<int> divisor = Divisor(M);

            Console.WriteLine(Solve(N, M, divisor));
            
        }
    }
}