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:



import java.util.*;

public class Main {

    private static Scanner sc = new Scanner(System.in);
    private static int N = 200000+69;
    private static long MOD = 1000000007;
    private static long mod = 998244353;
    private static int lcm = 720720;
    public static void main(String[] args)
    {
        int t=1;
      // t = sc.nextInt();
	   while(t-- > 0)
       {
           solve();
       }
    }
    private static void solve()
    {
        int m = sc.nextInt(), n = sc.nextInt();
        if(n%2 == 1)
        {
            int f=0;
            for(int i = 0;i<m;i++)
            {
                for(int j=0;j<n;j++)
                {
                    int x = sc.nextInt();
                    if(f==0) System.out.printf(lcm + " ");
                    else System.out.printf(lcm - x*x*x*x + " ");
                    f^=1;
                }
                System.out.printf("\n");
            }
        }
        else
        {
            int f=0;
            for(int i=0;i<m;i++)
            {
                int f1 =f;
                for(int j=0;j<n;j++)
                {
                    int x = sc.nextInt();
                    if(f1==0) System.out.printf(lcm + " ");
                    else System.out.printf(lcm - x*x*x*x + " ");
                    f1^=1;
                }
                f^=1;
                System.out.printf("\n");
            }
        }
    }
}