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: Runtime Error)


#include <stdio.h>

int main(void){
    int N,M;
    int a[10000]={0};
    int i,j,ans;

    scanf("%d %d",&N,&M);

    a[0]=(M-(N-1)*(N-1)/2)/N;

    for(i=0;i<N;i++) a[i]=a[0]+i;

    for(i=1;i<a[0];i++)
        for(j=0;j<N;j++){
            if(a[j]%i) break;
            else if(j==N-1) ans=i;
        }

    printf("%d",ans);

    

    return 0;
}