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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = (int)(0); i < (int)(n); i++)
#define repp(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define all(v) v.begin(), v.end())
using namespace std;
using lint     = long long;
const lint MOD = 1e9 + 7;
const lint INF = 1e18;

template <class T>
vector<T> dividers(T n) {
  vector<T> ret;
  for (T x = 1; x * x <= n; x++) {
    if (n % x == 0) { ret.push_back(x); }
  }
  return ret;
}

int main() {
  lint n, m;
  cin >> n >> m;
  vector<lint> v = dividers(m);

  lint ma = -1;
  for (auto x : v) {
    if (x * n <= m) { ma = max(ma, x); }
  }
  cout << ma << endl;
  return 0;
}