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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main(){
    int N, M, r, tmp, max = 0;
    int num1, num2, divi;

    cin >> N >> M;

    divi = M/N;

    while(divi > 0){
        num1 = divi;
        num2 = M - num1*(N - 1);

        if(num1 < num2){
            tmp = num1;
            num1 = num2;
            num2 = tmp;
        }
        r = num1 % num2;
        while(r!=0){
            num1 = num2;
            num2 = r;
            r = num1 %  num2;
        }
        if(num2 >= max){
            max = num2;
        }
        divi--;
    }
    cout << max << endl;
    return 0;
}