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:
/* 
 * created: 2021-02-12 16:42:12
**/

#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <vector>

#define x first
#define y second

using namespace std;

template<typename T, typename S> ostream& operator<<(ostream& os, const pair<T, S> &p) { return os << "(" << p.x << ", " << p.y << ")"; } 
template <class Ch, class Tr, class Container> basic_ostream <Ch, Tr> &operator << (basic_ostream <Ch, Tr> & os, Container const& x) { os << "{"; string sep; for(auto& y : x) os << sep << y, sep = ", "; return os << "}"; }

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int mod = 1e9 + 7, N = 550;

int n, m;

ll gcd(ll a, ll b) {
	return b ? a : gcd(a % b, b);
}

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

int g[N][N];
void solve() {
	ll ans = 1;
	for(int i = 1; i <= 16; i ++) ans = lcm(ans, i);

	cin >> n >> m;
	for(int i = 0; i < n; i ++)
		for(int j = 0; j < m; j ++) {
			cin >> g[i][j];
		}
	for(int i = 0; i < n; i ++) {
		for(int j = 0; j < m; j ++) {
			if((i + j) % 2 == 0) cout << ans << ' ';
			else cout << ans + pow(g[i][j], 4) << ' ';
		}
		cout << endl;
	}
}

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
#ifndef ONLINE_JUDGE
	const string filename = "cin";
	freopen((filename + ".in").c_str(), "r", stdin);
#endif
	int t;
	// cin >> t;
	t = 1;
	while(t --) {
		solve();
	}

	return 0;
}