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 A {
    static FastScanner fs;
    public static void main(String[] args) {
        fs=new FastScanner();
//        int t = fs.nextInt();
//        while (t-->0)
            solve();
    }
    public static void solve() {
        int n = fs.nextInt();
        int m = fs.nextInt();
        int[][] a = new int[n][m];
        for (int i=0; i<n; i++) a[i] = fs.readArray(m);
        int[][] b = new int[n][m];
        for (int i=0; i<n; i++) {
            for (int j = 0; j < m; j++) {
                if ((i + j) % 2 == 0)
                    b[i][j] = 720720-a[i][j]*a[i][j]*a[i][j]*a[i][j];
                else
                    b[i][j] = 720720;
            }
        }
        for (int i=0; i<n; i++) {
            for (int j = 0; j < m; j++) {
                if (j!=0) System.out.print(" ");
                System.out.print(b[i][j]);
            }
            System.out.println();
        }
    }
    static void ruffleSort(int[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    static final Random random =new Random();
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }

    static int[] reverse(int[] a) {
        int n=a.length;
        int[] res=new int[n];
        for (int i=0; i<n; i++) res[i]=a[n-1-i];
        return res;
    }
}