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, i;
	if(scanf("%d%d", &N, &M));
	for(i=N; i<=M/4; i++){
		if(M%i==0){
			printf("%d\n", M/i);
			return 0;
		}
	}
	if(M%3==0 && M/3>=N){
		printf("3\n");
		return 0;
	}
	if(M%2==0 && M/2>=N){
		printf("2\n");
		return 0;
	}
	printf("1\n");
	return 0;
}