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++ (GCC 9.2.1) (judge verdict: Accepted)

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

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

#define rep(i,cc,n) for(int i=cc;i<n;++i)
#define lrep(i,cc,n) for(long long i=cc;i<n;++i)
#define sqrep(i,cc,n) for(long long i=cc;i*i<=n;++i)
#define rrep(i,cc,n) for(long i=cc;i>n;--i)
#define pii pair<int, int>
#define pll pair<long long, long long>
 
using ll = long long;

const vector<int> dx = {1, 0, -1, 0};
const vector<int> dy = {0, 1, 0, -1};
const ll inf = 1001001001;
const ll e9  = 1000000000;
const ll mod = 1000000007;

ll gcd(ll x, ll y) { return (x % y)? gcd(y, x % y): y; }
int main() {
    ll n, m;
    cin >> n >> m;
    vector<ll>p;
    for(ll i=1; i*i<=m; i++){
        if(m%i==0){
            p.push_back(i);
            if(m!=i*i)p.push_back(m/i);
        }
    }
    sort(p.begin(),p.end(),greater<ll>());
    rep(i, 0, p.size()){
        if(p[i]*n<=m){
            cout << p[i] << endl;
            return 0;
        }
    }
}