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<set>
#include <bitset>
#include<queue>
#include<vector>
#include<map>
#include<stack>
#include <cstdio>
#include<algorithm>
#include <sstream>
#include<string>
#include<string.h>
#include <cmath>
#include <iomanip>
#include <string>
#include<list>
#include <limits>
#include <numeric>
#include <type_traits>
#define int long long
#define ll long long
#define mod  1000000007
#define inf 1e17
#define rep(i,j,n) for(int i=j;i<n;i++)
#define P pair<int,int>
#define ps push_back
double pi = 3.141592653589793;
using namespace std;
int z=0;
template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val){
    std::fill( (T*)array, (T*)(array+N), val );
}//ここから始めよう
signed main(){
    int a,b;cin>>a>>b;
    vector<int>v;
    for(int i=1;i*i<=b;i++){
        if(b%i==0){
            v.ps(i);v.ps(b/i);
        }
    }
    sort(v.begin(),v.end(),greater<int>());
    for(auto x : v){
        if(a*x<=b){
         cout<<x<<endl;return 0;
        }
    }
}