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>
#include <stdlib.h>
#include <math.h>
#include <stdbool.h>
#define PI 3.141592653589793238462643383279


void change(int *x, int *y){
	int z;
	z = *x;
	*x = *y;
	*y = z;
}
int compare_int(const void *a, const void *b){
	return *(int*)a - *(int*)b;
}
int gcd(int a, int b)
{
    int c;
    if (a < b) {
        a+=b; b=a-b; a-=b;
    }
    while (b != 0) {
        c = a % b;
        a = b;
        b = c;
    }
    return a;
}

int main(void){
int n,m;
	scanf("%d %d", &n, &m );
        if(n==1) printf("%d", m);
	else{for(int i=m/2+1;i>0;i--){
		if(m%i==0){
			if(m/i>=n){
				printf("%d",i);
				break;
			}
		}
	}}
	return 0;
}