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 D {
	public static int gcd(int a, int b){
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
	
    public static int lcm(int a, int b){
        return (a / gcd(a, b)) * b;
    }
    
    public static int pow_4(int num) {
    	return num*num*num*num;
    }
    
	public static void main(String[] args) {
		FastScanner fs = new FastScanner();
		FastOutput fo = new FastOutput();
		int n=fs.nextInt(),m=fs.nextInt();
		int arr[][]=new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				arr[i][j]=fs.nextInt();
			}
		}
		int LCM=1;
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				LCM=lcm(LCM,arr[i][j]);
			}
		}
		/*
		 * turns
		 * 0 -> l,l+x1^4,l,...
		 * 1 -> l+x2^4,l,l+x3^4,....
		 */
		int res[][]=new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				if((i%2==0 && j%2!=0) || (i%2!=0 && j%2==0)) {
					res[i][j]=LCM+pow_4(arr[i][j]);
				}
				else {
					res[i][j]=LCM;
				}
			}
		}
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				fo.print(res[i][j]+" ");
			}
			fo.println("");
		}
	}

	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

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

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

		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

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

	static class FastOutput {
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

		void print(String str) {
			try {
				bw.write(str);
				bw.flush();
			} catch (IOException e) {
			}
		}

		void print(int num) {
			try {
				bw.write((num + ""));
				bw.flush();
			} catch (IOException e) {
			}
		}

		void println(String str) {
			try {
				bw.write(str + '\n');
				bw.flush();
			} catch (IOException e) {
			}
		}

		void println(int num) {
			try {
				bw.write(num + "" + '\n');
				bw.flush();
			} catch (IOException e) {
			}
		}
	}
}