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 PYTHON3):

Solution:
def lcm(x ,y):
    return x*y//gcd(x,y)

def gcd(x, y):
    while y != 0:
        (x, y) = (y, x % y)
    return x

cumulcm=1
for i in range(1,17):
    cumulcm=lcm(cumulcm,i)
c=cumulcm
    
zs=[]
k=1
while k**4<10**6:
    zs.append(k**4)
    k+=1

# We can alternate between c and k*a[i,j], so long as (c-z)%y==0 then k=(c-z)//y.
alternateY=[-1 for _ in range(17)]
for y in range(1,17):
    ok=False
    for z in zs:
        if (c-z)%y==0:
            ok=True
            k=(c-z)//y
            break
    alternateY[y]=k*y
    assert ok==True #check that this is always possible.
    
def main():
    
    n,m=readIntArr()
    a=[]
    for _ in range(n):
        a.append(readIntArr())
    
    b=[[-1 for _ in range(m)] for __ in range(n)]
    for i in range(n):
        for j in range(m):
            if (i+j)%2==0:
                b[i][j]=c
            else:
                b[i][j]=alternateY[a[i][j]]
    multiLineArrayOfArraysPrint(b)
    
    
    return
    
#import sys
#input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
import sys
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
 
def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
 
inf=float('inf')
MOD=10**9+7
 
main()