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: Accepted)

#include <bits/stdc++.h>
#include <cstdio>
#include <string>

using namespace std;

#define INF 100000000
#define YJ 1145141919
#define INF_INT_MAX 2147483647
#define INF_LL_MAX 9223372036854775807
#define EPS 1e-10
#define MOD 1000000007
#define Pi acos(-1)
#define LL long long
#define ULL unsigned long long
#define LD long double

#define int long long

signed main()
{
    int N, M;
    cin >> N >> M;

    vector<int> mm;
    for(int i = 1; i <= sqrt(M); i++) {
        if(M%i == 0) {
            mm.push_back(i);
            mm.push_back(M/i);
        } 
    }

    sort(begin(mm), end(mm));
    for(int i = 0; i < mm.size(); i++) {
        cerr << mm[i] << endl;
    }
    auto it = upper_bound(begin(mm), end(mm), M/N);
    it--;
    cout << *it << endl;

    return 0;
}