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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>

#define N_MAX 100000

using namespace std;

int euclidean_gcd(int a, int b) {
  while(1) {
    if(a < b) swap(a, b);
    if(!b) break;
    a %= b;
  }
  return a;
}



int main(){
    int N, M;
    int div_max = 0;
    int div_tmp;
    cin >> N >> M;
    for(int i = 1; i*i <= M; i++){
        if(M%i == 0 && (M/i) >= N){
            div_tmp = euclidean_gcd(M/i, N)*i;
            if(div_tmp > div_max){
                div_max = div_tmp;
            }
        }
    }
    cout << div_max << '\n';
}