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 (GCC 5.4.1) (judge verdict: Accepted)

/*
 * main.c
 *
 *  Created on: 2019/02/21
 *      Author: family
 */


#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int data[100] = {0};

int main()
{
	int n, m;
	int val, val2, ans;
	int temp;
	scanf("%d %d", &n, &m);
	val = m/n;
	val2 = val + (m%n);

	if (val == val2) {
		ans = val;
	} else {
		temp = val;
		while(temp > 0) {
			if (m%temp == 0) {
				ans = temp;
				break;
			} else {
				temp--;
			}
		}
	}

	printf("%d\n",ans);
	return 0;
}