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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){
			int N = scan.nextInt();
			int M = scan.nextInt();

			//int[][]dp = new int[N][M];

			//dp[1][1] = 1;
			int max = 0;
			for(int i = 1;i<=N;i++) {
				if(M%i==0) {
					int wari = M/i;
					if(wari>=N) {
						max = i;
					}
				}
			}

			System.out.println(max);
		}


	}

	private static int gcd(int A,int B){//最大公約数
		return B==0?A:gcd (B,A%B);
	}


}