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<bits/stdc++.h>
using namespace std;
#define ll long long int
#define ld long double
#define pb push_back
#define mod 1000000007
#define inarr(i,arr,n); for(ll i=0;i<n;i++) cin >> arr[i];
#define outarr(i,arr,n); for(ll i=0;i<n;i++) cout<<arr[i]<<' ';
#define swap(a,b,t) {t=a;a=b;b=t;}
#define ve vector
#define sz(a) (int)((a).size())
#define fi first
#define se second
#define pa pair
#define all(x) x.begin(), x.end()
#define fastio  {ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);}
#define fr(i, a, b) for (ll i = a; i <= b; i++)
#define frn(i, a, b) for (ll i = a; i >= b; i--)
#define mk make_pair
#define ceil(x) (ll)(ceil(x))
#define endl "\n"
#define setvector(i, vname,value,size); for(ll i=0;i<size;i++)vname[i]=value;
const ll inf = 1e18;
ll gcd(ll a,ll b)
{
	if(a%b==0)
		return b;
	else
		return gcd(b,a%b);
}
int main()
{
    fastio
    ll n, m;
    cin>>n>>m;
    ve <ve <ll>> in(n, ve <ll>(m));
    fr(i, 0, n-1)
    {
        inarr(j, in[i], m);
    }
    ll fac16=1;
    fr(i, 2, 16)
    {
        fac16=(fac16*i)/gcd(fac16, i);
    }
    //cout<<fac16<<endl;
    ve <ve <ll>> ans(n, ve <ll>(m, fac16));
    fr(i, 0, n-1)
    {
        fr(j, 0, m-1)
        {
            if((i+j)%2)
            {
                ans[i][j]+=pow(in[i][j], 4);
            }
            cout<<ans[i][j]<<" ";
        }
        cout<<endl;
    }

}