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 java.math.*;
import java.math.BigInteger;


public final class A
{    
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<ArrayList<Integer>> g,tg;
	static long mod=998244353;
	static boolean set[],col[]; 
	static int par[];
	static pair size[],size1[];
	static char G[][];
	static int dp[][];
	//static Pair moves[]= {new Pair(-1,0),new Pair(1,0), new Pair(0,-1), new Pair(0,1)};
	public static void main(String args[])throws IOException
	{		
		int N=i(),M=i();
		int num=720720;
		int A[][]=new int[N][M];
		for(int i=0; i<N; i++)A[i]=input(M);
		for(int i=0; i<N; i++)
		{
			for(int j=0; j<M; j++)
			{
				if((i+j)%2==0)A[i][j]=num;
				else A[i][j]=(int)pow(A[i][j],4)+num;
				System.out.print(A[i][j]+" ");
			}
			System.out.println();			
		}
	}
	static int ask(int N)
	{
		System.out.println("? "+N);
		return i();
	}
	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static long mul(long a, long b)
	{
		return ( a %mod * 1L * b%mod )%mod;
	}
	static void swap(int A[],int a,int b)
	{
		int t=A[a];
		A[a]=A[b];
		A[b]=t;
	}


	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		int t=Math.min(a, b);
		b=Math.max(a, b);
		a=t;
		if(a!=b)
		{
			g.get(a).add(b);
			g.get(b).add(a);
			par[a]+=par[b];
			par[b]=a;
		}
	}
	static boolean isSorted(int A[])
	{
		for(int i=1; i<A.length; i++)
		{
			if(A[i]<A[i-1])return false;
		}
		return true;
	}

	static boolean isDivisible(StringBuilder X,int i,long num)
	{
		long r=0;
		for(; i<X.length(); i++)
		{
			r=r*10+(X.charAt(i)-'0');
			r=r%num;
		}
		return r==0;
	}    



	static int lower_Bound(int A[],int low,int high, int x) 
	{ 
		if (low > high) 
			if (x >= A[high]) 
				return A[high]; 

		int mid = (low + high) / 2; 

		if (A[mid] == x) 
			return A[mid]; 

		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
			return A[mid - 1]; 

		if (x < A[mid]) 
			return lower_Bound( A, low, mid - 1, x); 

		return lower_Bound(A, mid + 1, high, x); 
	} 

	static String f(String A)
	{
		String X="";
		for(int i=A.length()-1; i>=0; i--)
		{
			int c=A.charAt(i)-'0';
			X+=(c+1)%2;
		}
		return X;
	}

	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static String swap(String X,int i,int j)
	{
		char ch[]=X.toCharArray();
		char a=ch[i];
		ch[i]=ch[j];
		ch[j]=a;
		return new String(ch);
	}

	static int sD(long n)  
	{  

		if (n % 2 == 0 )  
			return 2;  

		for (int i = 3; i * i <= n; i += 2) {  
			if (n % i == 0 )  
				return i;  
		}  

		return (int)n;  
	}  

	static void setGraph(int N)
	{
		set=new boolean[N+1];
		col=new boolean[N+1];
		size=new pair[N+1];
		size1=new pair[N+1];
		g=new ArrayList<ArrayList<Integer>>();
		tg=new ArrayList<ArrayList<Integer>>();
		for(int i=0; i<=N; i++)
		{
			size[i]=new pair();
			size1[i]=new pair();
			g.add(new ArrayList<Integer>());
			tg.add(new ArrayList<Integer>());
		}
	}



	static  long pow(long a,long b)
	{
		//long mod=1000000007;
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}

	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}

	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}

	static long fact(long N)
	{ 
		long n=2; 
		if(N<=1)return 1;
		else
		{
			for(int i=3; i<=N; i++)n=(n*i)%mod;
		}
		return n;
	}

	static int kadane(int A[])
	{
		int lsum=A[0],gsum=A[0];
		for(int i=1; i<A.length; i++)
		{
			lsum=Math.max(lsum+A[i],A[i]);
			gsum=Math.max(gsum,lsum);
		}
		return gsum;
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static boolean isPrime(long N)
	{
		if (N<=1)  return false; 
		if (N<=3)  return true; 
		if (N%2 == 0 || N%3 == 0) return false; 
		for (int i=5; i*i<=N; i=i+6) 
			if (N%i == 0 || N%(i+2) == 0) 
				return false; 
		return true; 
	}
	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	static long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b );
	}

}

class pair implements Comparable<pair>
{
	long health,power;
	pair()
	{
		health=0;
		power=0;
	}
	pair(long h,long p)
	{
		health=h;
		power=p;
	}
	public int compareTo(pair X)
	{
		if(this.power>X.power)return 1;
		else if(this.power==X.power)return 0;
		else return -1;
	}
}

//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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;
	}

}