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 (Clang 3.8.0) (judge verdict: Accepted)


#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
 
using namespace std;
int n, m;
int ans;
 
int main()
{
    scanf("%d%d",&n,&m);
    int c = m/n;
    int b = sqrt(m);
    c = min(c, b);
    for (int i = 1; i * i <= m; ++i)
    {
        if (m % i == 0) 
        {
            int i1 = i;
            int i2 = m / i;
            if (i1 <= m / n) ans = max(ans, i1); 
            if (i2 <= m / n) ans = max(ans, i2);
        }
    }
    cout << ans;
}