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>
using namespace std;
#define ll long long

#define pii pair<int,int>
#define pll pair<ll,ll>

#define vi vector<int>
#define vll vector<ll>
#define vb vector<bool>
#define vpi vector<pii>
#define vpl vector<pll>
#define pb push_back
#define all(v) v.begin(),v.end()
#define fast_io ios_base::sync_with_stdio(false),cin.tie(NULL);


void cout_vector(vi v){
	
	for (ll unsigned i=0; i<v.size(); i++) cout << v[i] << " ";
	cout<<endl;
}

void cout_vector(vll v){
	
	for (ll unsigned i=0; i<v.size(); i++) cout << v[i] << " ";
	cout<<endl;
}

int sum_vector(vi v){
	return accumulate(all(v),0);
}

void sort_vector(vi&v){
	sort(all(v));
}

void sort_comp(vi &v, bool func(int,int)){
	sort(all(v),func);
}

bool comp(int a,int b){
	bool aend=0;
	
	if(a%2) a--,aend=1;
	if(b%2) b--;
	a/=2;
	b/=2;
	if(a==b){
		if(aend) return 1;
		return 0;
	}
	if(a<b) return 1;
	return 0; 
}

ll gcd(ll a, ll b){
	a=abs(a);
	b=abs(b);
	while(a){
		ll temp =a;
		a=b%a;
		b=temp;
	}
	return abs(b);
}

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

string binary(ll num){
	string ans="";
	do{
		ans=to_string(num%2)+ans;
		num/=2;
	}while(num);
	return ans;
}


const int mxn = 5e5+2;
const int mill = 1e6+3;
const ll mod = 1e9+7; 

ll pwr(ll num, ll p){
	ll res=1;
	while(p>0){
		if(p&1) res=(res*num)%mod;
		num=(num*num)%mod;
		p/=2;
	}
	return res;
}

ll inverse(ll num){
	return pwr(num,mod-2);
}



void solve(){
	int n,m;
	cin>>n>>m;
	int num;
	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			cin>>num;
			if((i+j)%2) cout<<720720<<" ";
			else cout<<720720+pwr(num,4)<<" ";
		}
		cout<<"\n";
	}
}



int main()
{
	
	fast_io
	int t;
	//cin>>t;
	t=1;
	while(t--) solve();
	
	
	return 0;
}