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 JAVA):

Solution:
//created by Whiplash99
import java.io.*;
import java.util.*;
public class D
{
    private static int _gcd(int a, int b) {return a==0?b:_gcd(b%a,a);}
    private static int _lcm(int a, int b){return a/_gcd(a,b)*b;}
    private static int pow4(int N){return N*N*N*N;}
    public static void main(String[] args) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        int lcm=1;
        for(i=1;i<=16;i++) lcm=_lcm(lcm,i);

        String[] s=br.readLine().trim().split(" ");
        N=Integer.parseInt(s[0]);
        int M=Integer.parseInt(s[1]);

        int[][] a=new int[N][M];
        for(i=0;i<N;i++)
        {
            s=br.readLine().trim().split(" ");
            for(int j=0;j<M;j++) a[i][j]=Integer.parseInt(s[j]);
        }

        int[][] ans=new int[N][M];
        for(i=0;i<N;i++)
        {
            for(int j=0;j<M;j++)
            {
                if(((i+j)&1)==1) ans[i][j]=lcm;
                else ans[i][j]=lcm+pow4(a[i][j]);
            }
        }

        StringBuilder sb=new StringBuilder();
        for(i=0;i<N;i++)
        {
            for(int j=0;j<M;j++) sb.append(ans[i][j]).append(" ");
            sb.append("\n");
        }
        System.out.println(sb);
    }
}