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;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 9223372036854775807;
    public static void Main()
    {
        long N = NextInt();
        long M = NextInt();
        List<int> memo = new List<int>();
        int m = (int)Math.Sqrt(M);
        for (int i = 1; i <= m; i++) { if (M % i == 0) memo.Add(i); }
        long ans = 1;
        foreach (var i in memo)
        {
            //Console.WriteLine(i + " : " + (M/i));
            if (i * N <= M) ans = Math.Max(i, ans);
            if ((M / i) * N <= M) ans = Math.Max(M / i, ans);
            //Console.WriteLine(ans);
        }
        Console.WriteLine(ans);
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}