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: Wrong Answer)

#include <iostream>
#include <stdio.h>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <cmath>
#include <limits.h>
#include <assert.h>
#include <bitset>
#include <deque>
#include <list>
#include <map>
#include <math.h>
#include <stack>
#include <queue>
#include <set>
#include <stdlib.h>
#include <string.h>

using namespace std;

#define mp make_pair
#define pb push_back
#define ll long long int
#define db double
#define ldb long double
#define MOD 1000000007
#define Fi first
#define Se second
#define INF INT_MAX
#define NINF INT_MIN
#define L_INF LLONG_MAX
#define L_NINF LLONG_MIN
#define gc getchar
#define sz(x) (int)(x).size()
#define pii pair<int,int>
#define pll pair<ll,ll>

void fsscan(){ios_base::sync_with_stdio(false);cin.tie(NULL);}

void scani(int &x)
{
    register int c = gc();x = 0;int neg = 0;
    for(;((c<48 || c>57) && c != '-');c = gc());
    if(c=='-') {neg=1;c=gc();}
    for(;c>47 && c<58;c = gc()) {x = (x<<1) + (x<<3) + c - 48;}
    if(neg) x=-x;
}

int main()
{
    fsscan();
    ll n,m;
    cin>>n>>m;
    
    for(ll i=m/2;i>=1;i--)
    {
        if((m%i==0)&&(m/i>=n))
        {
            cout<<i;
            return 0;
        }
    }
    
    return 0;
}