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<iostream>
#include <string> 
#include <vector>  
#include<math.h>
#include <algorithm>
#include<iomanip>
#include<map>
#define INF 1000000000
#define LM 55555
#define LL long long
using namespace::std;

long long now,D,H,a,p,t,A,T,x[101],y[101],h[101],num, N, K, M, ans;
string S;
bool xy[100][100][100];
char cc;


int main() {
	cin >> N>>M;
	if (N == 1) {
		cout << M << endl;
	}
	for (int i = 1; i < M; i++) {
		if (M%i == 0) {
			if (M / i < N) {
				cout << A << endl;
				return 0;
			}
			A = i;
		}
	}

	return 0;


	
}