#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <queue>
#include <iomanip>
#include <fstream>
#include <climits>
#include <cstdlib>
#include <stack>
 
  using namespace std;
   
// g++ -std=c++17 a.cpp
  typedef long long ll;
  typedef long double lld;
  int INF = INT_MAX-1;
  ll mod = 1e9+7;


ll gcd(ll a , ll b)
{
   if(b==0) return a;
   a%=b;
   return gcd(b,a);
}

 void solve(){

    int n,m;
    cin>>n>>m;
    vector<ll> a(n), b(m);
    for (int i =0; i<n; i++) cin>>a[i];
      for (int i =0; i<m; i++) cin>>b[i];
    if (n == 1){
      for (int i = 0; i<m; i++) cout<<a[0]+b[i]<<" ";
      cout<<"\n";
    return;
    }
    sort(a.begin(), a.end());
    ll g = a[1] - a[0];
    for (int i =1; i<n-1; i++) g = gcd(g, a[i+1] - a[i]);
    for (int i =0; i<m;i ++){
      cout<<gcd(gcd(a[0] + b[i], a[1] + b[i]), g)<<" ";
    }
    cout<<"\n";
  
 }

  int main()
  {
      ios_base::sync_with_stdio(0); cin.tie(0); 
      // ifstream in("promote.in");
      // cin.rdbuf(in.rdbuf());
      // ofstream out("promote.out");
      // cout.rdbuf(out.rdbuf());
     
     
   int q;
   q = 1;
   while(q--) solve();
   

}




### Prompt

Your challenge is to write a Cpp solution to the following problem:

You are given two positive integer sequences a_1, …, a_n and b_1, …, b_m. For each j = 1, …, m find the greatest common divisor of a_1 + b_j, …, a_n + b_j.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5).

The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10^{18}).

The third line contains m integers b_1, …, b_m (1 ≤ b_j ≤ 10^{18}).

Output

Print m integers. The j-th of them should be equal to GCD(a_1 + b_j, …, a_n + b_j).

Example

Input


4 4
1 25 121 169
1 2 7 23


Output


2 3 8 24

### Response

```cpp
#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <queue>
#include <iomanip>
#include <fstream>
#include <climits>
#include <cstdlib>
#include <stack>
 
  using namespace std;
   
// g++ -std=c++17 a.cpp
  typedef long long ll;
  typedef long double lld;
  int INF = INT_MAX-1;
  ll mod = 1e9+7;


ll gcd(ll a , ll b)
{
   if(b==0) return a;
   a%=b;
   return gcd(b,a);
}

 void solve(){

    int n,m;
    cin>>n>>m;
    vector<ll> a(n), b(m);
    for (int i =0; i<n; i++) cin>>a[i];
      for (int i =0; i<m; i++) cin>>b[i];
    if (n == 1){
      for (int i = 0; i<m; i++) cout<<a[0]+b[i]<<" ";
      cout<<"\n";
    return;
    }
    sort(a.begin(), a.end());
    ll g = a[1] - a[0];
    for (int i =1; i<n-1; i++) g = gcd(g, a[i+1] - a[i]);
    for (int i =0; i<m;i ++){
      cout<<gcd(gcd(a[0] + b[i], a[1] + b[i]), g)<<" ";
    }
    cout<<"\n";
  
 }

  int main()
  {
      ios_base::sync_with_stdio(0); cin.tie(0); 
      // ifstream in("promote.in");
      // cin.rdbuf(in.rdbuf());
      // ofstream out("promote.out");
      // cout.rdbuf(out.rdbuf());
     
     
   int q;
   q = 1;
   while(q--) solve();
   

}




```