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;

int gcd(int a,int b){
	return a%b==0?b:gcd(b,a%b);
}

int lcm(int a,int b){
	return a*b/gcd(a,b);
}

int main(){

	int n,m;
	cin >> n >> m;

	int a[n][m];

	for(int i=0;i<n;i++) for(int j=0;j<m;j++) cin >> a[i][j]; 

	int l = 1;
	
	for(int i=1;i<=16;i++){
		l = lcm(l,i);
	}

	int b[n][m];

	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			if((i+j)%2==0){
				b[i][j] = l;
			}else{
				b[i][j] = l + (a[i][j]*a[i][j]*a[i][j]*a[i][j]); // 16^4 + lcm(1,2,3,...,15,16) <= 10^16
			}
		}
	}

	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			cout << b[i][j] << " ";
		}
		cout << endl;
	}

	return 0;
}