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.io.*;
import java.util.*;

public class Solution {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
	    int n = sc.nextInt();
	    int m = sc.nextInt();
	    int[][] a = new int[n][m];
	    int[][] b = new int[n][m];
	    for(int i = 0; i< n ;i++) {
	       for(int j = 0; j< m ;j++) {
	           a[i][j] = sc.nextInt();
	           b[i][j] = 720720;
	       }
	    }
	    int[] ks = new int[31];
	    for (int i = 1; i < 32; i++)
	        ks[i - 1] = i * i * i * i;
        int idx = 0;
        while (idx <= m + n - 2) {
            for (int i = idx>=m ? idx- (m-1) :0; i <= idx && i < n; i++) {
               // System.out.println("idx: " + idx + " i: " + i);
                for (int k = 0; k < 31; k++) {
                   // System.out.println("ks[k]: " + ks[k]);
                    if (ks[k] % a[i][idx - i] == 0) {
                      //  System.out.println("div");
                        b[i][idx - i] -= ks[k];
                        break;
                    }
                }
            }
            idx += 2;
        }
        for (int[] i: b) {
            for (int j: i)
                System.out.print(j + " ");
            System.out.println();
        }
	}
}