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
#define _USE_MATH_DEFINES
#include <iostream>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <string>
#include <fstream>
#include <vector>
#include <queue>
#include <stack>
#include <sstream>
#include <list>
#include <map>
#include <set>
#include <limits>
#include <random>
#include <functional>
#include <unordered_set>
#include <unordered_map>
#include <cmath>

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef unsigned int ui;

#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vl vector<ll>

using namespace std;

const int N = 510;
const int M = 6;
const int MOD = 1000000007;
const int INF = 1009000999;
const ll LINF = (1ll << 60) + 1337;
const ld EPS = 0.00000001;

int gcd(int a, int b) {
	if (b == 0)
		return a;
	else
		return gcd(b, a % b);
}

int _lca(int a, int b) {
	return (a * 1ll * b) / gcd(a, b);
}

int a[N][N];
int n, m;

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#ifdef _DEBUG
	freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
#endif
	//#ifndef _DEBUG
	//	freopen("segmentupdate.in", "r", stdin); freopen("segmentupdate.out", "w", stdout);
	//#endif
	int lca = 1;
	for (int i = 2; i <= 16; i++) {
		lca = _lca(lca, i);
	}
	cin >> n >> m;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < m; j++) {
			cin >> a[i][j];
			if ((i + j) % 2) {
				cout << lca << " ";
			}
			else {
				cout << lca - pow(a[i][j], 4) << " ";
			}
		}
		cout << "\n";
	}
}


/*
	Important stuff
	- int overflow
	- array bounds
	- special cases (n=1, max n) maybe adhoc problem
	- doubles are read for a long time (4 * 10 ^ 5 danger GNU vs MS ICPC 2020 1/4)
	- don't get stuck on one approach
	- don't get stuck on one problem
	- recheck submissions if near the end of the tournament and there is nothing to do
	- do something instead of nothing and stay organized
*/