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.*;
import java.io.*;
public class D {

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int[] pow = new int[21];
		for(int i = 1; i <= 20; i++){
			pow[i] = i * i * i * i;
		}
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[][] arr = new int[n][m];
		for(int i = 0; i < n; i++){
			for(int j = 0; j < m; j++){
				arr[i][j] = sc.nextInt();
				if((i + j) % 2 == 0) arr[i][j] = 720720;
				else {
					arr[i][j] = 720720 - pow[arr[i][j]];
				}
			}
		}
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < n; i++){
			for(int j = 0; j < m; j++){
				sb.append(arr[i][j]+" ");
			}
			sb.replace(sb.length()-1, sb.length(), "\n");
		}
		PrintWriter pw = new PrintWriter(System.out);
		pw.println(sb.toString().trim());
		pw.flush();
	}
	static class Pair{
		int a, b;
		public Pair(int a, int b){
			this.a = a; this.b = b;
		}
		@Override
		public boolean equals(Object o){
			Pair p = (Pair)o;
			return a == p.a && b == p.b;
		}
		@Override
		public int hashCode(){
			return a + b;
		}
		public String toString(){
			return a + " " + b;
		}
	}
	
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch(IOException e) {
				throw new RuntimeException(e);
			}
		}
	}

}