Problem: Artem is building a new robot. He has a matrix a consisting of n rows and m columns. The cell located on the i-th row from the top and the j-th column from the left has a value a_{i,j} written in it. 

If two adjacent cells contain the same value, the robot will break. A matrix is called good if no two adjacent cells contain the same value, where two cells are called adjacent if they share a side. 

Artem wants to increment the values in some cells by one to make a good.

More formally, find a good matrix b that satisfies the following condition — 

  * For all valid (i,j), either b_{i,j} = a_{i,j} or b_{i,j} = a_{i,j}+1. 



For the constraints of this problem, it can be shown that such a matrix b always exists. If there are several such tables, you can output any of them. Please note that you do not have to minimize the number of increments.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10). Description of the test cases follows.

The first line of each test case contains two integers n, m (1 ≤ n ≤ 100, 1 ≤ m ≤ 100) — the number of rows and columns, respectively.

The following n lines each contain m integers. The j-th integer in the i-th line is a_{i,j} (1 ≤ a_{i,j} ≤ 10^9).

Output

For each case, output n lines each containing m integers. The j-th integer in the i-th line is b_{i,j}.

Example

Input


3
3 2
1 2
4 5
7 8
2 2
1 1
3 3
2 2
1 3
2 2


Output


1 2
5 6
7 8
2 1
4 3
2 4
3 2

Note

In all the cases, you can verify that no two adjacent cells have the same value and that b is the same as a with some values incremented by one. 

Solution (in PYTHON3):

Solution:
from sys import stdout, stdin, setrecursionlimit
from io import BytesIO, IOBase
from collections import *
from itertools import *
from random import * 
from bisect import *
from string import *
from queue import *
from heapq import *
from math import *
from re import *
from os import *

####################################---fast-input-output----#########################################


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = read(self._fd, max(fstat(self._fd).st_size, 8192))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = read(self._fd, max(fstat(self._fd).st_size, 8192))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


stdin, stdout = IOWrapper(stdin), IOWrapper(stdout)
graph, mod, szzz =  {}, 10**9 + 7, lambda: sorted(zzz())
def getStr(): return input()
def getInt(): return int(input())
def listStr(): return list(input())
def getStrs(): return input().split()
def isInt(s): return '0' <= s[0] <= '9'
def input(): return stdin.readline().strip()
def zzz(): return [int(i) for i in input().split()]
def output(answer, end='\n'): stdout.write(str(answer) + end)
def lcd(xnum1, xnum2): return (xnum1 * xnum2 // gcd(xnum1, xnum2))


dx = [-1, 1, 0, 0, 1, -1, 1, -1]
dy = [0, 0, 1, -1, 1, -1, -1, 1]
daysInMounth = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]


#################################################---Some Rule For Me To Follow---#################################
"""
    --instants of Reading problem continuously try to understand them.

    --If you Know some-one , Then you probably don't know him !

    --Try & again try, maybe you're just one statement away!


"""
##################################################---START-CODING---###############################################




# s = input().strip()

# n = len(s)

# class segTree:
#     def __init__(self):
#         self.a = [0]*(2*n)
#         self.b = [0]*(2*n)
#         self.c = [0]*(2*n)
    
#     def build(self, arr):
#         for i in range(n):
#             self.a[i+n] = 0
#             self.b[i+n] = 1 if arr[i] == '(' else 0
#             self.c[i+n] = 1 if arr[i] == ')' else 0
#         for i in range(n-1,0,-1):
#             to_match = min(self.b[i << 1],self.c[i << 1 | 1])
#             self.a[i] = self.a[i << 1] + self.a[i << 1 | 1] + 2*to_match
#             self.b[i] = self.b[i << 1] + self.b[i << 1 | 1] - to_match
#             self.c[i] = self.c[i << 1] + self.c[i << 1 | 1] - to_match
#     def query(self, l, r):  
#         left = []
#         right = []
#         l += n 
#         r += n 
#         while l <= r: 
#             if (l & 1): 
#                 left.append((self.a[l],self.b[l],self.c[l]))
#                 l += 1
#             if not (r & 1): 
#                 right.append((self.a[r],self.b[r],self.c[r]))
#                 r -= 1 
#             l >>= 1 
#             r >>= 1
#         a1 = b1 = c1 = 0
#         for a2, b2, c2 in left + right[::-1]:
#             to_match = min(b1,c2)
#             a1 += a2 + 2*to_match
#             b1 += b2 - to_match
#             c1 += c2 - to_match
#         return a1
# tree = segTree()
# tree.build(s)
# for m in range(getInt()):
#     l, r = zzz()
#     l -= 1
#     r -= 1
#     print(tree.query(l,r))
    
num = getInt()

for _ in range(num):
    n,m=zzz()
    for i in range(n):
        arr=zzz()
        for j in range(m):
            arr[j]+= (i+j)%2!=arr[j]%2
        print(*arr)