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:
#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <cmath>
#include <math.h>
#include <vector>
#include <algorithm>
#include <stack>
#include <set>
#include <ctime>
#include <queue>
#include <deque>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <random>
#include <cstdio>
#include <string>
#include <numeric>
#include <cctype>
#include <cassert>

#define double long double
//#define int long long
#define eb emplace_back
#define rs resize
#define ld long double
#define vi vector<int>
#define vpii vector<pair<int, int>>
#define ull unsigned long long


using namespace std;

// typedef long long ll;
// typedef vector<int> vi;
// typedef long double ld;

/*#pragma GCC optimize("Ofast")
#pragma GCC optimize("vpt")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("shrink-wrap-separate")
#pragma GCC optimize("loop-nest-optimize")
*/

int gcd(int a, int b) {
    if (!a)return b;
    return gcd(b % a, a);
}

int lcm(int a, int b) {
    return a * b / gcd(a, b);
}

void solve() {
    int n, m;
    cin >> n >> m;
    int lc = 1;
    gcd(3, 2);
    for (int i = 2; i <= 16; i++) {
        lc = lcm(lc, i);
    }

    vector<vi> a(n, vi(m));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cin >> a[i][j];
        }
    }

    vector<vi> b(n, vi(m));

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            if ((i + j) % 2 == 0) {
                cout << lc << ' ';
            }
            else {
                cout << lc + (int)(pow(a[i][j], 4)) << ' ';
            }
        }
        cout << "\n";
    }

} 


signed main() {
    // freopen("‪", "r", stdin);
    //freopen("C:\\Users\\Asus\\Desktop\\input.txt", "w", stdout);
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cout << fixed;
    cout.precision(30);
    int t = 1;
    //cin >> t;
    while (t--)
        solve();
    //   system("pause");
}