AtCoder Grand Contest 001 - Arrays and Palindrome

Snuke got a present from his mother on his birthday. The present was a pair of two sequences a and b, consisting of positive integers. They satisfied all of the following properties:

* The sum of all elements of a is N.
* The sum of all elements of b is N.
* Any string of length N that satisfies the following two conditions (1) and (2) will also satisfy the condition (3).
* (1) Any of the following forms a palindrome: the first a_1 letters, the following a_2 letters, the following a_3 letters and so on.
* (2) Any of the following forms a palindrome: the first b_1 letters, the following b_2 letters, the following b_3 letters and so on.
* (3) All N letters are the same.



He was happy, until one day he lost both of the sequences. Now, he only remembers that the sequence a was a permutation of another sequence A of length M.

To bring him happiness again, his mother has decided to give him another pair of sequences a and b that satisfies his favorite properties and is consistent with his memory.

Constraints

* 1≦N≦10^5
* 1≦M≦100
* 1≦A_i≦10^5
* The sum of all A_i equals N.

Input

The input is given from Standard Input in the following format:


N M
A_1 A_2 ... A_M


Output

If there exists a pair of sequences a and b that satisfies the properties and is consistent with Snuke's memory, print three lines. The first line must contain the sequence a, the second line must contain the length of the sequence b, and the third line must contain the sequence b.

If such a pair does not exist (because Snuke's memory is wrong or some other reason), print a single line containing the word `Impossible` (case-sensitive).

Examples

Input

3 2
2 1


Output

1 2
1
3


Input

6 1
6


Output

6
3
1 2 3


Input

55 10
1 2 3 4 5 6 7 8 9 10


Output

Impossible

Source: atcoder | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
(n, m) = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
breakFlag = False
for i in range(1, m - 1):
	if a[i] % 2 == 1:
		if a[0] % 2 == 1:
			if a[len(a) - 1] % 2 == 1:
				print('Impossible')
				breakFlag = True
				break
			else:
				(a[i], a[len(a) - 1]) = (a[len(a) - 1], a[i])
		else:
			(a[i], a[0]) = (a[0], a[i])
if breakFlag == False:
	ans = ''.join([str(s) + ' ' for s in a])
	print(ans[:-1])
	if m == 1:
		if a[0] > 1:
			a[0] -= 1
			a.append(1)
			print(m + 1)
		else:
			print(m)
	elif a[len(a) - 1] == 1:
		print(m - 1)
		a.pop()
		a[0] += 1
	else:
		print(m)
		a[0] += 1
		a[len(a) - 1] -= 1
	ans = ''.join([str(s) + ' ' for s in a])
	print(ans[:-1])


(n, m) = map(int, input().split())
ali = list(map(int, input().split()))
if m == 1 and ali[0] == 1:
	print(1)
	print(1)
	print(1)
	exit()
if m == 1:
	print(ali[0])
	print(2)
	print(ali[0] - 1, 1)
	exit()
flag = 0
c = []
for a in ali:
	if a % 2 == 1:
		if flag == 0:
			lm = a
			flag += 1
		elif flag == 1:
			rm = a
			flag += 1
		elif flag == 2:
			print('Impossible')
			exit()
	else:
		c.append(a)
if flag == 0:
	lm = c[0]
	del c[0]
	rm = c.pop()
if flag == 1:
	rm = c.pop()
b = [lm + 1] + c
d = [lm] + c + [rm]
if rm > 1:
	b.append(rm - 1)
print(' '.join(map(str, d)))
print(len(b))
print(' '.join(map(str, b)))


import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 7)
(N, M) = map(int, readline().split())
A = [int(x) for x in readline().split()]
OD = [x for x in A if x & 1]
EV = [x for x in A if not x & 1]
if len(OD) >= 3:
	print('Impossible')
	exit()
if len(A) == 1:
	if N == 1:
		B = [1]
	else:
		B = [1, N - 1]
elif len(OD) == 0:
	B = A.copy()
	B[0] -= 1
	B[-1] += 1
elif len(OD) == 1:
	A = OD + EV
	B = A.copy()
	B[0] += 1
	B[-1] -= 1
else:
	A = [OD[0]] + EV + [OD[-1]]
	B = A.copy()
	B[0] += 1
	B[-1] -= 1
B = [x for x in B if x > 0]
print(*A)
print(len(B))
print(*B)


(n, m) = map(int, input().split())
a = list(map(int, input().split()))
b = []
o = []
for i in a:
	if i % 2:
		o.append(i)
	else:
		b.append(i)
if len(o) > 2:
	print('Impossible')
	exit()
if len(o) == 1:
	b = o + b
elif len(o) == 2:
	b = [o[0]] + b + [o[1]]
ans = []
for i in range(len(b)):
	if i == 0:
		ans.append(b[i] - 1)
	elif i == len(b) - 1:
		ans.append(b[i] + 1)
	else:
		ans.append(b[i])
anss = []
for i in ans:
	if i != 0:
		anss.append(i)
if sum(anss) != n:
	anss.append(n - sum(anss))
print(*b)
print(len(anss))
print(*anss)


import sys

def solve(n, m, arr):
	odds = []
	evens = []
	for a in arr:
		if a % 2 == 0:
			evens.append(a)
		else:
			odds.append(a)
	if len(odds) > 2:
		print('Impossible')
		return
	if len(odds) == 2:
		(o1, o2) = odds
		aaa = [o1] + evens + [o2]
		bbb = [2] * (o1 // 2 + 1)
		bbb += evens
		bbb += [2] * (o2 // 2)
	elif len(odds) == 1:
		if odds[0] == 1:
			aaa = odds + evens
			bbb = evens + odds
		elif evens:
			aaa = odds + evens
			bbb = [odds[0] - 1] + evens[:-1] + [evens[-1] + 1]
		else:
			aaa = odds
			bbb = [odds[0] // 2, odds[0] // 2 + 1]
	else:
		aaa = evens
		bbb = [1] + evens[:-1] + [evens[-1] - 1]
	print(*aaa)
	print(len(bbb))
	print(*bbb)
(n, m, *aaa) = map(int, sys.stdin.buffer.read().split())
solve(n, m, aaa)


def solve(n, m, a):
	odd = []
	even = []
	for a_i in a:
		if a_i % 2 == 0:
			even += [a_i]
		else:
			odd += [a_i]
	if len(odd) >= 3:
		return None
	(a, b) = ([], [])
	if odd:
		x = odd.pop()
		a += [x]
		b += [x - 1]
	else:
		x = even.pop()
		a += [x]
		b += [x - 1]
	a += even
	b += even
	if odd:
		x = odd.pop()
		a += [x]
		b += [x + 1]
	else:
		b += [1]
	return (a, b)
(n, m) = map(int, input().split())
a = list(map(int, input().split()))
it = solve(n, m, a)
if it is None:
	print('Impossible')
else:
	(a, b) = it
	b = list(filter(lambda b_i: b_i, b))
	print(*a)
	print(len(b))
	print(*b)


from sys import exit
(n, m) = map(int, input().split())
a = list(map(int, input().split()))
odd = []
even = []
for x in a:
	if x % 2 == 0:
		even.append(x)
	else:
		odd.append(x)
if n % 2 == 0:
	if len(odd) > 2:
		print('Impossible')
		exit()
	if len(odd) == 2:
		a = [odd[0]] + even + [odd[1]]
		b = [odd[0] + 1] + even + [odd[1] - 1]
		if b[-1] == 0:
			b.pop()
	else:
		a = even
		b = [1] + even
		b[-1] -= 1
		if b[-1] == 0:
			b.pop()
else:
	if len(odd) > 1:
		print('Impossible')
		exit()
	if m == 1:
		b = [1, n - 1]
	else:
		a = odd + even
		b = [odd[0] + 1] + even
		b[-1] -= 1
	if b[-1] == 0:
		b.pop()
print(*a)
print(len(b))
print(*b)


(S, N) = map(int, input().split())
A = list(map(int, input().split()))
O = [a for a in A if a % 2 == 1]
E = [a for a in A if a % 2 == 0]
if len(O) > 2:
	print('Impossible')
else:
	A = O[:min(len(O), 1)] + E + O[min(1, len(O)):]
	B = A[:] + ([0] if len(A) == 1 else [])
	B[0] -= 1
	B[-1] += 1
	if B[0] == 0:
		B = B[1:]
	print(' '.join((str(a) for a in A)))
	print(len(B))
	print(' '.join((str(b) for b in B)))