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 9.2.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <tuple>
#include <vector>
using namespace std;
typedef long long ll;
ll const INF = 1LL << 60;

vector<ll> divisor(int n) {
  vector<ll> res;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      if (i != n / i) res.push_back(n / i);
    }
  }
  return res;
}

int main() {
  ll N, M;
  cin >> N >> M;
  vector<ll> divs = divisor(M);
  ll ans = 1;
  for (auto d : divs) {
    if (M / d >= N) ans = max(ans, d);
  }
  cout << ans << endl;
  return 0;
}