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 sc scanf
#define pr printf
#define ls rt<<1
#define rs rt<<1|1
typedef long long ll;
typedef double db;
const ll inf=1ll<<58;
const int N=1e3+10;
const int mod=1e9+7;
typedef pair<int,int> pii;

int a[N][N],b[N][N];
void solve(){
	int n,m;
	sc("%d%d",&n,&m);
	for(int i=1;i<=n;++i)
		for(int j=1;j<=m;++j){
			sc("%d",&a[i][j]);
			if((i+j)&1)
				b[i][j]=720720;
			else
				b[i][j]=720720+a[i][j]*a[i][j]*a[i][j]*a[i][j];
			pr("%d%c",b[i][j]," \n"[j==m]);
		}
}

signed main()
{
	int T;
//	sc("%d",&T);
	T=1;
	while(T--)solve();
	return 0;
}