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;

#define ll long long int
#define vi vector<int>
#define vll vector<ll>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define vii vector<pii>
#define uset unordered_set
#define heap priority_queue
#define pb push_back
#define mkp make_pair
#define ff first
#define ss second
#define endl "\n"
#define all(x) x.begin(),x.end()
#define sortall(x) sort(all(x))
#define sortrev(x) sort(all(x), greater<int>())
#define op(x) cout<<x<<endl
#define show(x) cout << (#x) << " : " << x << endl
#define speedhack ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define YesNo(condition) cout<< (condition ? "Yes" : "No") << "\n"
#define YESNO(condition) cout<< (condition ? "YES" : "NO") << "\n"

#define MOD 1000000007
#define MAX 200005

void magic();

int main(){
	speedhack;
	#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
	#endif
	int t=1;

	// cin>>t;
	
	while(t--) magic();
    return 0;
}

void magic(){
	ll n,m;
	cin>>n>>m;
	vvl arr(n,vll(m));
	for(ll i=0;i<n;i++){
		for(ll j=0;j<m;j++){
            cin>>arr[i][j];
            if((i+j)%2==0){
            	arr[i][j] = 720720;
            }else{
            	arr[i][j] = 720720 + (arr[i][j]*arr[i][j]*arr[i][j]*arr[i][j]);
            }
            cout<<arr[i][j]<<" ";
        }
        cout<<endl;
	}

}