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 Solution {
	 public static void main(String[] args) throws Exception
    {
		     FastReader fr=new FastReader();
		     
		    int n=fr.nextInt();
		      int m=fr.nextInt();
		      
		     int lcm=720720;
		      for(int i=0;i<n;i++) {
		    	  for(int j=0;j<m;j++) {
		    		  int d=fr.nextInt();
		    		  if((i+j)%2==0)
		    			  System.out.print(lcm+" ");
		    		  else
		    			  System.out.print((lcm-d*d*d*d)+" ");
		    			  
		    	  }
		    	  System.out.println();
		      }
		      
		      
		      
		}
	
	
	 public static int findGCD(int a,int b) {
		 if(b == 0)
		      return a;
		    
		    return findGCD(b, a%b);
	 }
	
	
	
 }
 
	 
 class Pair implements Comparable<Pair>{
	 int x;
	 int y;
	 Pair(int x,int y){
		 this.x=x;
		 this.y=y;
	 }
	 public int compareTo(Pair o) {
		 if(this.x!=o.x)
			 return this.x-o.x;
		 else
			 return this.y-o.y;
	 }
	 
 }

  

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;
    }
}