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:
'''print((2 ** 4) * 3 * 3 * 5 * 7 * 11 * 13)
n = 1
while n ** 4 < (2 ** 4) * 3 * 3 * 5 * 7 * 11 * 13:
    z = (2 ** 4) * 3 * 3 * 5 * 7 * 11 * 13 - (n ** 4)
    Z = int(z)
    for i in range(2, Z + 1):
        while z % i == 0:
            print(i, end=' ')
            z //= i
    print()
    n += 1'''
n, m = map(int, input().split())
A = []
B = []
for i in range(n):
    A.append(list(map(int, input().split())))
    B.append([0] * m)
for i in range(n):
    for j in range(m):
        if (i + j) % 2 == 0:
            B[i][j] = 720720
        else:
            if A[i][j] == 1:
                B[i][j] = 2 * 2 * 2 * 2 * 2 * 2 * 11261
            elif A[i][j] == 2:
                B[i][j] = 2 * 2 * 2 * 2 * 2 * 2 * 11261

            elif A[i][j] == 3:
                B[i][j] = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 1249

            elif A[i][j] == 4:
                B[i][j] = 2 * 2 * 2 * 2 * 2 * 2 * 11261


            elif A[i][j] == 5:
                B[i][j] = 710720
            elif A[i][j] == 6:
                B[i][j] = 699984
            elif A[i][j] == 7:
                B[i][j] = 106064
            elif A[i][j] == 8:
                B[i][j] = 2 * 2 * 2 * 2 * 2 * 2 * 11261
            elif A[i][j] == 9:
                B[i][j] = 388944
            elif A[i][j] == 10:
                B[i][j] = 710720
            elif A[i][j] == 11:
                B[i][j] = 706079
            elif A[i][j] == 12:
                B[i][j] = 719424
            elif A[i][j] == 13:
                B[i][j] = 263744


            elif A[i][j] == 14:
                B[i][j] = 106064
            elif A[i][j] == 15:
                B[i][j] = 670095
            elif A[i][j] == 16:
                B[i][j] = 682304
for i in range(len(B)):
    print(*B[i])