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)

#include <stdio.h>

int main() {
	int n, m, d1, d2, ans;

	scanf("%d%d", &n, &m);
	ans = 1;
	for (d1 = 1; d1 <= m / d1; d1++)
		if (m % d1 == 0) {
			if (m / d1 >= n && ans < d1)
				ans = d1;
			d2 = m / d1;
			if (m / d2 >= n && ans < d2)
				ans = d2;
		}
	printf("%d\n", ans);
	return 0;
}