Problem: You are given a matrix a consisting of positive integers. It has n rows and m columns.

Construct a matrix b consisting of positive integers. It should have the same size as a, and the following conditions should be met: 

  * 1 ≤ b_{i,j} ≤ 10^6; 
  * b_{i,j} is a multiple of a_{i,j}; 
  * the absolute value of the difference between numbers in any adjacent pair of cells (two cells that share the same side) in b is equal to k^4 for some integer k ≥ 1 (k is not necessarily the same for all pairs, it is own for each pair). 



We can show that the answer always exists.

Input

The first line contains two integers n and m (2 ≤ n,m ≤ 500).

Each of the following n lines contains m integers. The j-th integer in the i-th line is a_{i,j} (1 ≤ a_{i,j} ≤ 16).

Output

The output should contain n lines each containing m integers. The j-th integer in the i-th line should be b_{i,j}.

Examples

Input


2 2
1 2
2 3


Output


1 2
2 3


Input


2 3
16 16 16
16 16 16


Output


16 32 48
32 48 64


Input


2 2
3 11
12 8


Output


327 583
408 664

Note

In the first example, the matrix a can be used as the matrix b, because the absolute value of the difference between numbers in any adjacent pair of cells is 1 = 1^4.

In the third example: 

  * 327 is a multiple of 3, 583 is a multiple of 11, 408 is a multiple of 12, 664 is a multiple of 8; 
  * |408 - 327| = 3^4, |583 - 327| = 4^4, |664 - 408| = 4^4, |664 - 583| = 3^4. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()

const int maxn = 720720;

int f(int x){
    return x * x * x * x;
}

void solve(){
    
    int n, m; cin >> n >> m;
    vector< vector< int > > a(n, vector< int >(m));
    for(auto& v : a){ for(auto& u : v) { cin >> u; }}
    for(int i = 0; i < n; ++i){
        for(int j = 0; j < m; ++j){
            if((i + j) & 1){
                cout << maxn << ' ';
            } else {
                cout << maxn + f(a[i][j]) << ' ';
            }
        }
        cout << '\n';
    }
    
}


int main(){
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif

    ios_base::sync_with_stdio(false); cin.tie(0);

    int t = 1;
    // cin >> t;


    for(int i = 1; i <= t; i++){
        // cout << "Case #" << i << ": ";

        solve();

    }
    return 0;
}