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: Time Limit Exceeded)

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

int isPrime(int a){
	if(a % 2 == 0)return 0;
	int lim = (int)sqrt(a);
	for(int i = 3; i < lim; i += 2){
		if(a % i == 0)return 0;
	}
	return 1;
}

int main(void){
	int n, m;
	scanf("%d %d", &n, &m);
	int res = 0;
	/*
	if(isPrime(m)){
		printf("1\n");
		return 0;
	}
	*/
	int i = 0;
	while(m % (n + i))i++;
	printf("%d\n", m / (n + i));
	return 0;
}