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: Wrong Answer)

// AtCoder ABC112: D - Partition
// 2020.1.29 bal4u

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

int main()
{
	int i, b, N, M, ans;
	
	scanf("%d%d", &N, &M);
	ans = 1, b = (int)sqrt((double)M);
	for (i = 2; i <= b; ++i) {
		if (M%i == 0) {
			if (M/i >= N && i > ans) ans = i;
			if (i >= N && M/i > ans) ans = M/i;
		}
	}
	printf("%d\n", ans);
	return 0;
}