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:
//189301019.akshay
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.Random;
import java.util.Arrays;
import java.util.StringTokenizer; 
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Collections;

public class D 
{ 
    public static void main(String[] args) 
	{ 
		FastReader sc=new FastReader(); 
		StringBuffer ans=new StringBuffer();
		int test=1;
		while(test-->0)
		{
			int n=sc.nextInt(),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();
				}
			}
		
			
			int brr[][]=new int[n][m];
			int a=720720;
			
			for(int i=0;i<n;i++) {
				if(i%2 == 0) {
					for(int j=0;j<m;j++) {
						if(j%2 == 0) brr[i][j]=a;
						else brr[i][j]=a-(int)Math.pow(arr[i][j], 4);
					}
				}
				else {
					for(int j=0;j<m;j++) {
						if(j%2 == 0) brr[i][j]=a-(int)Math.pow(arr[i][j], 4);
						else brr[i][j]=a;
					}
				}
			}
				
			for(int i=0;i<n;i++) {
				for(int j=0;j<m;j++)
					ans.append(brr[i][j]+" ");
				ans.append("\n");
			}
			
		
		}
	    System.out.print(ans);
	} 
    
    static int _lcm(int a,int b) {
    	return (a*b)/_gcd(a,b);
    }
    static int _gcd(int a,int b) {
    	if(b ==0 ) return a;
    	return _gcd(b,a%b);
    }
    static int find(int a,int b,int root) {
    	for(int i=1;root*i<=1000000;i++) {
    		int mul =root*i;
    		double op1 = Math.pow(Math.abs(mul-a), 0.25);
    		double op2 = Math.pow(Math.abs(mul-b), 0.25);
    		if(op1 != 0 && op1 == (long)(op1) && (op2) == (long)(op2)) {
    			return mul;
    		}
    	}
    	return 1;
    }
    static int find(int a,int root) {
    	for(int i=1;root*i<=1000000;i++) {
    		int mul =root*i;
    		double op1 = Math.pow(Math.abs(mul-a), 0.25);
    		if(op1 != 0 && op1 == (long)(op1)) {
    			return mul;
    		}
    	}
    	return 1;
    }
    
    
    static final Random random=new Random();
    
	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 void ruffleSort(long[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n);
			long temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	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; 
		} 
	} 


}