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:
import sys
import os.path
from collections import *
import math
import bisect

if(os.path.exists('input.txt')):
    sys.stdin = open("input.txt","r")
    sys.stdout = open("output.txt","w")
else:
    input = sys.stdin.readline

sqrt = math.sqrt
gcd = math.gcd

############## Code starts here ##########################

num = 1
for i in range(2,17):
    num = num*i//gcd(num,i)

m,n = [int(x) for x in input().split()]
arr = [0]*m
for i in range(m):
    arr[i] = [int(x) for x in input().split()]
res = 0
for i in range(m):
    for j in range(res,n,2):
        arr[i][j] = num
    res = 1-res

res = 1
for i in range(m):
    for j in range(res,n,2):
        arr[i][j] = num - arr[i][j]**4
    res = 1-res

for i in range(m):
    for j in range(n):
        print(arr[i][j],end=" ")
    print()

############## Code ends here ############################