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 collections
import string
import math
import copy
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


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 = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            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 = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            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:
            os.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")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)


def input(): return sys.stdin.readline().rstrip("\r\n")


mo = 998244353


def exgcd(a, b):
    if not b:
        return 1, 0
    y, x = exgcd(b, a % b)
    y -= a//b * x
    return x, y


def getinv(a, m):
    x, y = exgcd(a, m)
    return -(-1) if x == 1 else x % m


def comb(n, b):
    res = 1
    b = min(b, n-b)
    for i in range(b):
        res = res*(n-i)*getinv(i+1, mo) % mo
        # res %= mo
    return res % mo


def quickpower(a, n):
    res = 1
    while n:
        if n & 1:
            res = res * a % mo
        n >>= 1
        a = a*a % mo
    return res


def dis(a, b):
    return abs(a[0]-b[0]) + abs(a[1]-b[1])


def getpref(x):
    if x > 1:
        return (x)*(x-1) >> 1
    else:
        return 0


def orafli(upp):
    primes = []
    marked = [False for i in range(upp+3)]
    for i in range(2, upp):
        if not marked[i]:
            primes.append(i)
        for j in primes:
            if i*j >= upp:
                break
            marked[i*j] = True
            if i % j == 0:
                break
    return primes
history = {}
askctr = 0
def ask(s):
    global askctr, history
    if s in history:
        return history[s]
    askctr+=1
    print(f"? {s}", flush=True)
    ret = int(input())
    hisadd(s, ret)
    chkans(s)
    return ret

def answer(s):
    print(f"! {s}", flush=True)
    # return int(input())


def getans(history, l, r):
    for i in range(l, r+1):
        ask(i)
        history[i] = int(input())
        if i==2:
            if 1 in history:
                if history[2]>history[1]:
                    answer(1)
                    return
        else:
            if i-1 in history and i-2 in history:
                if history[i-1]<history[i-2] and history[i-1]<history[i]:
                    answer(i-1)
                    return

def chkans(i):
    global history, n
    if i==1:
        if history.get(2,0)>history.get(1,999999999):
            answer(1)
            exit(0)
            return True
    elif i==n:
        if history.get(n-1,0)>history.get(n,999999999):
            answer(n)
            exit(0)
            return True
    elif history.get(i-1, 0) > history.get(i, 99999999) < history.get(i+1, 0):
        if 0<i<=n:
            answer(i)
            exit(0)
            return True
    return False


def hisadd(pos, val):
    global history
    if val == 1:
        answer(pos)
        exit(0)
        return True
    else:
        history[pos] = val
        return chkans(pos)

def solve():

    A, B = map(int, input().split())
    # tot = B*(B+1)>>1
    tot = 0
    p = B-1-(A-2)
    i = 1
    while 1:
        # tot-=p
        d = min(A//i-1-i, B-i)
        if d>0:
            tot+=d
        else:
            break
        i+=1
    print(tot)
    # a = [int(i) for i in input().split()]
    # b = [math.ceil(int(i)/A) for i in input().split()]
# n = int(input())
# p1 = ask(1)
# hisadd(1, p1)
# p2 = ask(n)
# hisadd(n, p2)

# solve(1,n)
# t = int(input())

# for ti in range(t):
#     solve()

mmp = []
for i in range(0,17):
    mmp.append(i**4)

n,m = map(int,input().split())
ma = []
for i in range(n):
    l = [int(i) for i in input().split()]
    ma.append(l)
mp = [[720720 for j in range(m)] for i in range(n)]
for i in range(n):
    for j in range(m):
        if (i^j)&1:
            mp[i][j]-=mmp[ma[i][j]]

for i in mp:
    print(*i)