You are given an $array$ of size $N$ and an integer $K$ ( $N > 1 , K > 0$ ).
Each element in the array can be incremented by $K$ or decremented by $K$ $at$ $most$ $once$.
So there will be  $3^n$ possible combinations of final array. (As there are 3 options for every element).

Out of these combinations, you have to select a combination, in which the $absolute$ difference between the largest and the smallest element is $maximum$.
You have to print the $maximum$ $absolute$ $difference$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a two lines of input
- First line contains two integers $N, K$. 
- Second line contains $N$ space separated integers.

-----Output:-----
For each testcase, output the maximum absolute difference that can be achieved on a new line.

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq N \leq 1000$
- $1 \leq K , arr[i]  \leq 10000$
$NOTE$:  Large  input files, Use of fastio is recommended.

-----Sample Input:-----
2

4 3

4 2 5 1

3 5

2 5 3

-----Sample Output:-----
10

13

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
testcases = int(input())
for _ in range(testcases):
	(N, K) = list(map(int, input().split()))
	array = list(map(int, input().split()))
	max = array[0]
	min = array[0]
	for i in array:
		if i > max:
			max = i
		if i < min:
			min = i
	max = max + K
	min = min - K
	print(abs(max - min))


t = int(input())
for i in range(t):
	(n, k) = list(map(int, input().split()))
	lst = list(map(int, input().split()))
	print(abs(min(lst) - k) + (max(lst) + k))


for _ in range(int(input())):
	(n, k) = map(int, input().split())
	arr = list(map(int, input().split()))
	maxv = max(arr)
	minv = min(arr)
	print(abs(maxv + k - (minv - k)))


t = int(input())
for i in range(t):
	l = list(map(int, input().split()))
	n = l[0]
	k = l[1]
	m = list(map(int, input().split()))
	print(abs(max(m) + k - (min(m) - k)))


a = int(input())
z = []
for i in range(a):
	b = input().split()
	c = list(map(int, input().split()))
	z.append(max(c) - min(c) + 2 * int(b[1]))
for i in z:
	print(i)


for i in range(int(input())):
	(N, K) = map(int, input().split())
	lst = list(map(int, input().split()))
	p = max(lst) + K
	q = min(lst) - K
	print(abs(p - q))


t = int(input())
for _ in range(t):
	(n, k) = map(int, input().split())
	arr = list(map(int, input().split()))[:n]
	m = max(arr)
	mi = min(arr)
	a = m - mi + 2 * k
	print(a)


t = int(input())
while t > 0:
	t -= 1
	(n, k) = map(int, input().split())
	a = list(map(int, input().split()[:n]))
	mx = max(a) + k
	mn = min(a) - k
	print(mx - mn)


t = int(input())
while t > 0:
	t -= 1
	(n, k) = map(int, input().split())
	a = list(map(int, input().split()[:n]))
	m1 = max(a)
	m2 = min(a)
	m1 = m1 + k
	m2 = m2 - k
	print(m1 - m2)


try:
	for _ in range(int(input())):
		(n, k) = map(int, input().split())
		li = list(map(int, input().split()))
		a = max(li)
		b = min(li)
		c = a + k
		d = b - k
		print(c - d)
except:
	pass


try:
	for _ in range(int(input())):
		(n, k) = [*map(int, input().split())]
		t = [*map(int, input().split())]
		a = max(t) + k
		b = min(t) - k
		if b > 0:
			print(abs(a - b))
		else:
			print(abs(b - a))
except:
	pass


def __starting_point():
	t = int(input())
	for _ in range(t):
		(n, k) = map(int, input().split())
		A = [int(i) for i in input().split()]
		print(max(A) - min(A) + 2 * k)
__starting_point()


for _ in range(int(input())):
	(n, k) = map(int, input().split())
	l = list(map(int, input().split()))
	r = max(l) - min(l) + 2 * k
	print(r)


for testcase in range(int(input())):
	(n, k) = map(int, input().split())
	arr = list(map(int, input().split()))
	(maxv, minv) = (max(arr), min(arr))
	print(maxv - minv + 2 * k)


t = int(input())
for _ in range(t):
	(n, k) = map(int, input().split())
	array = list(map(int, input().split()))
	print(max(array) - min(array) + 2 * k)


for T in range(int(input())):
	(N, K) = map(int, input().split())
	L = list(map(int, input().split()))
	m = max(L) + K
	s = min(L) - K
	print(m - s)


for _ in range(int(input())):
	(n, increment) = list(map(int, input().split()))
	arr = list(map(int, input().split()))
	arr.sort()
	longVal = arr[-1] + increment
	shortVal = arr[0] - increment
	print(abs(longVal - shortVal))


try:
	for _ in range(int(input())):
		(n, k) = map(int, input().split())
		l = input().split()
		l = [int(i) for i in l]
		m = max(l)
		m += k
		mi = min(l)
		mi -= k
		print(m - mi)
except EOFError:
	pass


t = int(input())
for i in range(t):
	(n, k) = map(int, input().split())
	z = list(map(int, input().split()))
	a = min(z) - k
	b = max(z) + k
	print(abs(b - a))


for _ in range(int(input())):
	(n, k) = map(int, input().split())
	l = list(map(int, input().split()))[:n]
	l.sort()
	a = l[0] - k
	b = l[-1] + k
	print(b - a)


for i in range(int(input())):
	(n, k) = list(map(int, input().split()))
	l = list(map(int, input().split()))
	ma = max(l) + k
	mi = min(l) - k
	print(abs(ma - mi))


try:
	t = int(input())
	for i in range(t):
		(n, k) = map(int, input().split())
		l = [int(x) for x in input().split()]
		print(abs(max(l) + k - (min(l) - k)))
except EOFError:
	pass


t = int(input())
for i in range(0, t):
	(n, k) = list(map(int, input().split()))
	x = list(map(int, input().split()))
	a = max(x) + k
	b = min(x) - k
	print(a - b)


for _ in range(int(input())):
	(n, k) = map(int, input().split())
	arr = list(map(int, input().split()))
	arr.sort(reverse=True)
	if arr[0] >= 0:
		arr[0] = arr[0] + k
	elif arr[0] < 0:
		arr[0] -= k
	if arr[len(arr) - 1] >= 0:
		arr[len(arr) - 1] -= k
	elif arr[len(arr) - 1] < 0:
		arr[len(arr) - 1] -= k
	print(abs(arr[0] - arr[len(arr) - 1]))


for i in range(int(input())):
	(n, k) = list(map(int, input().split()))
	a = list(map(int, input().split()))
	z = max(a) + k
	m = min(a) - k
	sum = abs(z) + abs(m)
	print(sum)