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 A {

    static int gcd(int a, int b) {
        if (a == 0)
            return b;

        return gcd(b % a, a);
    }

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

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();

        int lcm = 1;

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

        int n = sc.nextInt();
        int m = sc.nextInt();

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {

                int cur = sc.nextInt();

                if ((i + j) % 2 == 0) {
                    sb.append(lcm).append(" ");
                } else {
                    sb.append(lcm + (long) Math.pow(cur, 4)).append(" ");
                }

            }
            sb.append("\n");
        }

        System.out.print(sb);
    }
}