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.*;
import static java.lang.Math.max;
import static java.lang.Math.min;

public class CP{
    static int MAX = Integer.MAX_VALUE, MIN = Integer.MIN_VALUE;
    static FastScanner sc = new FastScanner();
    static PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] args){
    		solve();
        out.close();
    }
    
    static void solve() {
    	int n = sc.nextint(), m = sc.nextint();
    	for(int i = 0; i < n; ++i) {
    		for(int j = 0; j < m; ++j) {
    			int k = sc.nextint();
    			if((i+j)%2 == 0) {
    				out.print(720720 + " ");
    			}
    			else {
    				out.print((720720-k*k*k*k) + " ");
    			}
    		}
    		out.println();
    	}
    }
    
    static void sort(int[] a) {
        Random r = new Random();
        int n = a.length;
        for(int i = 0; i < n; ++i) {
            int idx = r.nextInt(n);
            int temp = a[idx];
            a[idx] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }
    
    static BufferedReader br;
    static StringTokenizer st;
    
    static class FastScanner{
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next() {
            while(st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int[] readint(int n) {
            int[] res = new int[n];
            for(int i = 0; i < n; i++) {
                res[i] = nextint();
            }
            return res;
        }
        
        long[] readlong(int n) {
            long[] res = new long[n];
            for(int i = 0; i < n; i++) {
                res[i] = nextlong();
            }
            return res;
        }
        
        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;
        }
    }
}