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<stdbool.h>
#include<string.h>
#include<math.h>
#define mprint(x) printf(FORMATCONVERSION(x),(x))
#define FORMATCONVERSION(x) _Generic((x),\
                                    int:"%d",unsigned int:"%u",\
                                    double:"%lf",long long int:"%lld",\
                                    unsigned long long int:"%llu",\
                                    char :"%c",char*:"%s")


int main(void){
    unsigned n,m;
    scanf("%u %u",&n,&m);

    unsigned ans;

    for(unsigned i = m / n;i > 0;i--)if(m % i == 0){ans = i;break;}

    mprint(ans);
    return 0;
}