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 <bits/stdc++.h> 
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define all(vec) vec.begin(), vec.end()
#define tmax(x,y,z) max((x),max((y),(z)))
#define tmin(x,y,z) min((x),min((y),(z)))
typedef long long ll;ll MM = 1000000000;ll mod = MM + 7; ll MMM=9223372036854775807;//2^63 -1
ll GCD(ll x, ll y) {if (x % y == 0) return y;else return GCD(y, x % y);}
ll LCM(ll x, ll y) { return x * y / GCD(x, y);}
//cout << fixed << setprecision(10);

int main(){
  ll n,m; cin>>n>>m;
  ll t=m/n;
  while(1){
    if((m-n*t)%t==0){
    cout<<t<<endl; return 0;
    }
    t--;
  }
}