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;
namespace Myatcoder
{
    public class Program
    {
        public static void Main()
        {
            int[] A = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            int maxValue = 0;
            if (A[0] != 1) {
                for (int i = 1; i <= A[1]; i++)
                {
                    if (A[0] * i > A[1]) break;
                    if (A[1] % i == 0) maxValue = i;
                }
                Console.WriteLine(maxValue);
            } else {
                Console.WriteLine(A[1]);
            }
        }
    }
}