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)

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

int main(){
    int N, M;
    int i, j, k;
    int div, sqrM;
    int ans;

    scanf("%d %d", &N, &M);
    div = M/N;
    sqrM =(int)sqrt(M);

    i=1;

    while(i<=sqrM){
        if(M%i == 0 && M/i < div){
            ans = M/i;
        }else if(M%i == 0 && i<=div){
            ans = i;
        }
        i++;
    }
    printf("%d", ans);

    return 0;

}