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.BufferedReader;
import java.io.InputStreamReader;

public class D {

    static class Pair {
        long a;
        long b;

        public Pair(long a, long b) {
            this.a = a;
            this.b = b;
        }
    }

    public static void main(String[] args) throws Exception {
        // write your code here
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        long c = lcm(16);
        int[] nm = getArray(reader.readLine());
        int n = nm[0];
        int m = nm[1];
        for (int i = 0; i < n; i++) {
            int[] t = getArray(reader.readLine());
            for (int j = 0; j < m; j++) {
                long ans = 0;
                if ((i + j) % 2 == 0) {
                    ans = (int) c;
                } else {
                    ans = (int) (c + Math.pow(t[j], 4));
                }
                System.out.print(ans + " ");
            }
            System.out.println();
        }
    }

    static long lcm(int max) {
        int res = 1;
        for (int i = 2; i <= max; i++) {
            res = res * (i / gcd(res, i));
        }
        return res;
    }

    private static int gcd(int res, int i) {
        if (res == 0) return i;
        return gcd(i % res, res);
    }

    private static int[] getArray(String readLine) {
        String strings[] = readLine.split(" ");
        int n = strings.length;
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(strings[i]);
        }
        return a;
    }

    private static long[] getLongArray(String readLine) {
        String strings[] = readLine.split(" ");
        int n = strings.length;
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(strings[i]);
        }
        return a;
    }

    private static int getInt(String s) {
        try {
            return Integer.parseInt(s);
        } catch (Exception e) {
            return 0;
        }
    }

    private static long getLong(String s) {
        try {
            return Long.parseLong(s);
        } catch (Exception e) {
            return 0;
        }
    }

    private static double getDouble(String s) {
        try {
            return Double.parseDouble(s);
        } catch (Exception e) {
            return 0;
        }
    }

}