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 <bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//using namespace __gnu_pbds;
using namespace std;
typedef long long ll;
typedef long double ld;
//typedef tree<int,null_type,less<int >,rb_tree_tag,tree_order_statistics_node_update>indexed_set;
template<class T1, class T2>
ostream &operator <<(ostream &os, pair<T1,T2>&p);
template <class T>
ostream &operator <<(ostream &os, vector<T>&v);
template <class T>
ostream &operator <<(ostream &os, set<T>&v);
template <class T1, class T2>
ostream &operator <<(ostream &os, map<T1,T2>&v);
#ifdef APURBA
#define HERE cout<<"here - "<<__LINE__<<"\n";
#define debug(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }
void err(istream_iterator<string> it)
{
    cout<<endl;
}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args)
{
    cout << *it << " = " << a << " ";
    err(++it, args...);
}
#else
#define HERE
#define debug(args...)
#endif
const ll N = 1e6;
const ll mod = 1e9+7;
typedef pair<int,int> pii;




void TEST_CASES(int cas)
{
    ll n,m;
    cin>>n>>m;
    vector<vector<ll> >a(n,vector<ll>(m));
    vector<vector<ll> >b(n,vector<ll>(m));
    for(ll i=0;i<n;i++)
    {
        for(ll j=0;j<m;j++)
        {
            cin>>a[i][j];
        }
    }
    ll now =0;
    ll val = 720720;
    for(ll i=0;i<n;i++)
    {
        ll turn = now;
        for(ll j=0;j<m;j++)
        {
            if(turn==0)
            {
                b[i][j] = val;
            }
            else{
                ll eta = a[i][j];
                for(ll x= 1;;x++)
                {
                    ll bal = val + (x*x*x*x);
                    if(bal %eta==0)
                    {
                        b[i][j] = bal;
                        break;
                    }
                }
            }
            turn = 1-turn;
        }
        now = 1-now;

    }
    for(ll i=0;i<n;i++)
    {
        for(ll j=0;j<m;j++)
        {
            cout<<b[i][j]<<" ";
        }
        cout<<"\n";
    }

}




/*

*/

int32_t main()
{
#ifndef APURBA
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#endif
    //freopen("input.txt","r",stdin);
    //freopen("out1.txt","w",stdout);
    int t=1,cas=0;
    //cin>>t;
    while(t--)
    {
        TEST_CASES(++cas);
    }
    return 0;
}



template<class T1, class T2>
ostream &operator <<(ostream &os, pair<T1,T2>&p)
{
    os<<"{"<<p.first<<", "<<p.second<<"} ";
    return os;
}
template <class T>
ostream &operator <<(ostream &os, vector<T>&v)
{
    os<<"[ ";
    for(int i=0; i<v.size(); i++)
    {
        os<<v[i]<<" " ;
    }
    os<<" ]";
    return os;
}

template <class T>
ostream &operator <<(ostream &os, set<T>&v)
{
    os<<"[ ";
    for(T i:v)
    {
        os<<i<<" ";
    }
    os<<" ]";
    return os;
}
template <class T1, class T2>
ostream &operator <<(ostream &os, map<T1,T2>&v)
{
    for(auto i:v)
    {
        os<<"Key : "<<i.first<<" , Value : "<<i.second<<endl;
    }
    return os;
}