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: Accepted)

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
#include<queue>
#include<set>
#include<map>
#include<stack>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pII;
#define pb push_back
#define X first
#define Y second
#define mp make_pair
#define clr(x,y) memset(x,y,sizeof(x))
#define FOR(i, x, y) for (decay<decltype(y)>::type i = (x), _##i = (y); i < _##i; ++i)
#define FORD(i, x, y) for (decay<decltype(x)>::type i = (x), _##i = (y); i > _##i; --i)
const int inf=0x3f3f3f3f;
const ll mod=1e9+7;
const int maxn=1e6+5;
//ll fmod(ll x,ll y){ll res=1;while(y){if(y&1)res=res*x%mod;y>>=1;x=x*x%mod;}return res;}
//ll gcd(ll x,ll y){return y==0?x:gcd(y,x%y);}
int main()
{
int n,m;
while(cin>>n>>m)
{
    int ans = 1;
    for(int i = 1; i*i <= m; ++i)
    {
        if((m%i) == 0)
        {
            if(m/i >= n)
                ans = max(i,ans);
            if(m/(m/i) >= n)
                ans = max(ans,(m/i));
                //cout<<i<<"  "<<ans<<endl;
        }
    }
    cout<<ans<<endl;
}
}