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: Runtime Error)

#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;
}
typedef long long int ll;

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define MOD (1000000007)
#define ALL(v) (v).begin(), (v).end()
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

vector<ll> divisor(ll n)
{
    vector<ll> ret;
    for (ll i = 1; i * i <= n; i++)
    {
        if (n % i == 0)
        {
            ret.push_back(i);
            if (i * i != n)
                ret.push_back(n / i);
        }
    }
    sort(begin(ret), end(ret));
    return (ret);
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll n, m;
    cin >> n >> m;
    vector<ll> yakusu = divisor(m);
    ll ok = 0;
    ll ng = (int)yakusu.size() + 1;
    while (llabs(ok - ng) > 1)
    {
        ll mid = (ok + ng) / 2;
        ll tmp = m / yakusu[mid];
        if (tmp >= n)
        {
            ok = mid;
        }
        else
        {
            ng = mid;
        }
    }
    cout << yakusu[ok] << endl;
}