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 CPP):

Solution:
//#pragma GCC optimize(3)
#include <bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define inf 0x3f3f3f3f
#define INF 0x7fffffff
#define infll 0x3f3f3f3f3f3f3f3f
#define il inline
#define re register
#define pb push_back
#define db double
#define ll long long
#define ull unsigned long long
#define pii pair<int,int>
#define pll pair<ll,ll>
#define puu pair<ull,ull>
#define MP make_pair
#define lowbit(x) x&(-x)
#define fi first
#define se second
il ll read()
{
	char ch = getchar();
	ll p = 1,data = 0;
	while(ch<'0'||ch>'9')
	{
		if(ch == '-')p = -1;
		ch = getchar();
	}
	while(ch>='0'&&ch<='9')
	{
		data = data*10+(ch^48);
		ch = getchar();
	}
	return p*data;
}
il ll gcd(ll a,ll b)
{
	if(!a || !b) return (!a)?b:a;
	while(b ^= a ^= b ^= a %= b);
	return a;
}
il ll lcm(ll a,ll b)
{
	return a*b/gcd(a,b);
}
void exgcd(ll a, ll b, ll &x,ll &y)
{
	if(!b) x = 1, y = 0;
	else
	{
		exgcd(b, a % b, y, x);
		y -= x * (a / b);
	}
}
il ll qpow(ll a,ll b)
{
	ll r = 1;
	while(b)
	{
		if(b&1)r = a*r;
		a = a*a;
		b>>=1;
	}
	return r;
}
const int mod = 1e9+7,maxn = 505;
int mp[maxn][maxn],b = 720720;
int main()
{
	int n = read(),m = read();
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= m; j++)
			mp[i][j] = read();
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= m; j++)
			printf("%d%s",b+((i+j)%2?qpow(mp[i][j],4):0),j==m?"\n":" ");		
	return 0;
}
/*

*/