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>
using namespace std;

long long gcd(long long a, long long b) {
    if(a == 1 || b == 1){
        return 1;
    }
    if(a < b) gcd(b, a);
    long long r;
    while ((r=a%b)) {
        a = b;
        b = r;
    }
    return b;
}

int main(){
    int n, m;
    cin >> n >> m;
    int c = 0, hokan,ans = 0;
    for(int i = 1; i <= 1145141919810; i++){
        hokan = 0;
        ans = i;
        for(int j = 1; j<= n; j++){
            hokan += i*j;
            if(i < n){
                ans = gcd(ans,i*(j+1));
            }
        }
        if(hokan <= m){
            c = ans;
        } else {
            break;
        }
    }
    cout << c << endl;
    return 0;
}