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:
#include<iostream>
#include<string>
#include<algorithm>
#include<map>
#include<unordered_map>
#include<vector>
#include<set>
#include<queue>
#include<stack>
#include <math.h>
#include<climits>
//#include <ext/pb_ds/assoc_container.hpp>
//using namespace __gnu_pbds;
using namespace std;
#define ll long long
#define ff first
#define ss second
#define pb push_back
#define deb(x) cout<<x<<"\n";
#define deB(x,y) cout<<x<<" "<<y<<"\n";
#define Deb(x,y,z) cout<<x<<" "<<y<<" "<<z<<"\n";
#define YES cout<<"YES\n";
#define Yes cout<<"Yes\n";
#define NO cout<<"NO\n";
#define No cout<<"No\n";
#define clt(x) 63-__builtin_clzll(x)
#define bct(x) __builtin_popcountll(x)
#define all(v) (v).begin(),(v).end()
#define pi pair<ll,ll>
#define vi vector<ll>
#define vpi vector<pair<ll,ll>>
#define maxq priority_queue<ll>
#define minq priority_queue<ll,vector<ll>, greater<ll>>
#define cont continue;
#define reto return 0;
#define sz size()
#define spmod 1116295198451
#define mod 1000000007
#define md 998244353 
#define N 200009
//typedef tree<int,null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> //pbds;
ll a[509][509];
int main()
{
  ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
  #ifndef ONLINE_JUDGE
  	freopen("input.txt", "r", stdin);
  	freopen("output.txt", "w", stdout);
  #endif
  ll n,m;
  cin>>n>>m;
  ll i=0,j;
  while(i<n)
  {
  	j=0;
  	while(j<m)
  	{
  		cin>>a[i][j];
  		j++;
  	}
  	i++;
  }
  i=0;
  while(i<n)
  {
  	j=0;
  	while(j<m)
  	{
  		if((i+j)%2)
  			cout<<720720-a[i][j]*a[i][j]*a[i][j]*a[i][j]<<" ";
  		else 
  			cout<<"720720 ";
  		j++;
  	}
  	cout<<"\n";
  	i++;
  }
}