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 PYTHON):

Solution:
#####################################   
import atexit, io, sys, collections, math, heapq,fractions
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
####################################

def check(v,n, bb):
	
	return v and n/v == n%v and (v <= bb)
def count(n, bb):
	c = 0
	d = 1
	while(d*d <= n):
		if n % d == 0:
			for v in set([d, n/d]):
				q = (n/v) -1
				if (0<q <= bb) and check(q, n ,bb):c+=1
				#if 0< v-1 <= bb and check(v-1,n, bb):c += 1
		if d > bb+1:
			break
		
		d +=1 
	return c

def f(a):
	for u in range(1,30):
		if (u ** 4) % a == 0:
			return  u ** 4
	return -1
def gcd(a,b):
	return gcd(b, a%b) if b else a
def lcm(a,b):
	return a * b / gcd(a,b)

n,m = map(int ,raw_input().split())
for i in range(n):
	l = map(int, raw_input().split())
	l = [720720 + (f(l[j]) if (i+j)%2  else 0) for j in range(len(l))]
	print ' '.join(map(str, l))