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:

//package _701;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.nio.file.Paths;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Main4 {

	public Main4() throws FileNotFoundException {

//		File file = Paths.get("input.txt").toFile();
//		if (file.exists()) {
//			System.setIn(new FileInputStream(file));
//		}
		long t = System.currentTimeMillis();

		FastReader reader = new FastReader();

		int n = reader.nextInt();

		int m = reader.nextInt();
		int[][] a = new int[n][m];
		int lcm=1;
		
		for(int i=2;i<=16;i++) {
			lcm=lcm(i,lcm);
		}
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				a[i][j] = reader.nextInt();
			}
		}
		//System.out.println(lcm);
		int[][] b=new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				int res=0;
				if((2+i+j)%2==0) {
					res=lcm;
				}else {
					int v=a[i][j]*a[i][j];
					res=lcm+v*v;
				}
				System.out.print(res+" ");
			}
			System.out.println();
		}
		
		
		



	}
	
	private int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

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

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	public static void main(String[] args) throws FileNotFoundException {
		new Main4();
	}

}