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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;


int main(){
  long long n,m;
  scanf ("%lld %lld",&n,&m);
  vector<int>a(m/n+2,0);
  vector<int>b;
  a[0]=0;
  a[1]=0;
  for(long long t=min(m/n+2,m-n+1);t>0;t--){
    if(m%t==0){
      printf("%lld\n",t);
      return 0;
    }
  }
}