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>
#define ll long long
#define INF 1000000
#define MAXN 505
#define Pii pair<ll,ll>
#define pb push_back

using namespace std;

ll n,m,a[MAXN][MAXN],b[MAXN][MAXN],d[20];
vector<ll> A;

ll UCLN(ll a, ll b){
    if(a==b) return a;
    if(a>b)
        UCLN(a-b,b);
    else
        UCLN(a,b-a);
}
ll BCNN(ll a, ll b){
    return (a*b/UCLN(a,b) );
}

ll BCNN_Mang(){
    ll temp = BCNN(A[0], A[1] );
    for(ll i=2;i<A.size();i++){
        temp = BCNN(temp, A[i]);
    }
    return temp;
}

int main()
{
    //ifstream cin("Multiples&PowerDifferences.inp");
    //ofstream cout("Multiples&PowerDifferences.out");
    cin >> n >> m;
    for(ll i=1; i<=n; i++){
        for(ll j=1; j<=m; j++){
            cin >> a[i][j];
            if(d[a[i][j]]==0){
                d[a[i][j]]=1;
                A.pb(a[i][j]);
            }
        }
    }
    ll U;
    if(A.size()==1) U=A[0];
    else U=BCNN_Mang();

    for(ll i=1; i<=n; i++){
        for(ll j=1; j<=m; j++){
            if(i%2==1){
                if(j%2==1) b[i][j]=U;
            }
            else if(i%2==0){
                if(j%2==0) b[i][j]=U;
            }
        }
    }
    for(ll i=1; i<=n; i++){
        for(ll j=1; j<=m; j++){
            if(b[i][j]==U) continue;
            for(ll k=1; k<=30; k++){
                ll x=k*k*k*k;
                bool check=false;
                ll x1=U+x;
                if(x1<=INF){
                    if(x1%a[i][j]==0){
                        b[i][j]=x1;
                        check=true;
                    }
                }
                if(check) break;
                ll x2=U-x;
                if(x2>=1){
                    if(x2%a[i][j]==0){
                        b[i][j]=x2;
                        check=true;
                    }
                }
                if(check) break;
            }
        }
    }
    for(ll i=1; i<=n; i++){
        for(ll j=1; j<=m; j++){
            cout << b[i][j] << ' ';
        }
        cout << '\n';
    }
    return 0;
}