It's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh. 

In this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes the first and the second integer from from the board, on the second move he removes the first and the second integer of the remaining sequence from the board, and so on. Bimokh stops when the board contains less than two numbers. When Bimokh removes numbers x and y from the board, he gets gcd(x, y) points. At the beginning of the game Bimokh has zero points.

Mashmokh wants to win in the game. For this reason he wants his boss to get exactly k points in total. But the guy doesn't know how choose the initial sequence in the right way. 

Please, help him. Find n distinct integers a1, a2, ..., an such that his boss will score exactly k points. Also Mashmokh can't memorize too huge numbers. Therefore each of these integers must be at most 109.

Input

The first line of input contains two space-separated integers n, k (1 ≤ n ≤ 105; 0 ≤ k ≤ 108).

Output

If such sequence doesn't exist output -1 otherwise output n distinct space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Examples

Input

5 2


Output

1 2 3 4 5


Input

5 3

Output

2 4 3 7 1

Input

7 2


Output

-1

Note

gcd(x, y) is greatest common divisor of x and y.

Difficulty: MEDIUM
Tags: Number theory

Constructive algorithms

Starter code:

Solutions:
(n, k) = map(int, input().split())
if n // 2 > k or (k != 0 and n == 1):
	print(-1)
	exit(0)
ans = [0] * n
ans[0] = k - n // 2 + 1
if n > 1:
	ans[1] = 2 * ans[0]
	for i in range(2, n):
		ans[i] = ans[i - 1] + 1
print(*ans)


(n, k) = [int(c) for c in input().split()]
res = []
pairs = n // 2
if pairs == 0 and k == 0:
	print('42')
elif pairs == 0 or pairs > k:
	print('-1')
else:
	avg = k // pairs
	max = 0
	for i in range(1, pairs):
		max = avg * (2 * i + 1)
		res.append(avg * (2 * i))
		res.append(max)
	rest = avg + k % pairs
	t1 = max // rest + 1
	i = pairs
	res.append(rest * t1)
	res.append(rest * (t1 + 1))
	if n % 2 == 1:
		res.append(1)
	print(' '.join(map(str, res)))


(n, k) = map(int, input().split())
ans = [(1000000000 - 2 * i, 1000000000 - 2 * i - 1) for i in range(n // 2 - 1)] + [(k - (n // 2 - 1), 2 * (k - (n // 2 - 1)))]
if k < n // 2 or (k > 0 and n == 1):
	print(-1)
else:
	print(' '.join(['%d %d' % (ans[i][0], ans[i][1]) for i in range(n // 2)]) + (' 100500' if n % 2 == 1 else ''))


(n, k) = map(int, input().split())
if k == 0 and n == 1:
	print(1)
elif n // 2 > k or n == 1:
	print(-1)
else:
	x = k - n // 2 + 1
	print(x, x * 2, *range(x * 2 + 1, x * 2 + 1 + n - 2))


(n, k) = map(int, input().split())
if n // 2 > k or (n == 1 and k != 0):
	print(-1)
elif n == 1 and k == 0:
	print(1)
else:
	ext = k - n // 2 + 1
	ans = [ext, 2 * ext]
	n -= 2
	for i in range(1, 100001, 2):
		if n <= 1:
			break
		if i not in ans and i + 1 not in ans:
			print(i, i + 1, end=' ')
			n -= 2
	print(*ans, end=' ')
	if n & 1:
		print(1000000000)


(n, k) = tuple(map(int, input().split()))
if n % 2:
	pairs = (n - 1) // 2
else:
	pairs = n // 2
if pairs > k or (not pairs and k > 0):
	print(-1)
else:
	if pairs < k:
		answer = [k - pairs + 1]
		answer.append(answer[0] * 2)
		answer += [i for i in range(answer[1] + 1, answer[1] + n - 1)]
	else:
		answer = [i for i in range(1, n + 1)]
	print(' '.join(map(str, answer)))


(n, k) = map(int, input().split())
ans = []
if n == 1:
	if k == 0:
		print(1)
	else:
		print(-1)
elif k < n // 2:
	print(-1)
else:
	ans.append(k + 1 - n // 2)
	ans.append(2 * ans[0])
	for i in range(2, n):
		ans.append(ans[-1] + 1)
	print(*ans)


def numbers(n, k):
	if k == 0 and n == 1:
		return [1]
	if n == 1 or k < n // 2:
		return [-1]
	(result, t) = (list(), k - (n - 2) // 2)
	result.append(t)
	result.append(2 * t)
	for i in range(n - 2):
		result.append(2 * t + i + 1)
	return result
(N, K) = [int(j) for j in input().split()]
print(*numbers(N, K))


class InputHandlerObject(object):
	inputs = []

	def getInput(self, n=0):
		res = ''
		inputs = self.inputs
		if not inputs:
			inputs.extend(input().split(' '))
		if n == 0:
			res = inputs[:]
			inputs[:] = []
		while n > len(inputs):
			inputs.extend(input().split(' '))
		if n > 0:
			res = inputs[:n]
			inputs[:n] = []
		return res
InputHandler = InputHandlerObject()
g = InputHandler.getInput
(n, k) = [int(x) for x in g()]
if k < n // 2:
	print(-1)
elif n == 1:
	if k == 0:
		print(1)
	else:
		print(-1)
else:
	m = k + 1 - n // 2
	r = [m, 2 * m]
	if m < 10 ** 6:
		r += [10 ** 7 + i for i in range(n - 2)]
	else:
		r += [1 + i for i in range(n - 2)]
	print(' '.join((str(x) for x in r)))


(n, k) = [int(i) for i in input().split()]
if n == 1 and k == 0:
	print(1)
elif n == 1 and k > 0:
	print(-1)
elif k < n // 2:
	print(-1)
elif n >= 2:
	if n % 2 == 0:
		m = n - 2
		summ = 0
		st = 10 ** 8
		while m > 0:
			print(st, end=' ')
			st += 1
			print(st, end=' ')
			summ += 1
			st += 1
			m -= 2
		diff = k - summ
		print(diff, diff * 8)
	else:
		m = n - 3
		summ = 0
		st = 10 ** 8
		while m > 0:
			print(st, end=' ')
			st += 1
			print(st, end=' ')
			summ += 1
			st += 1
			m -= 2
		diff = k - summ
		print(diff, diff * 8, end=' ')
		print(diff * 8 + 1)


(n, k) = list(map(int, input().split()))
if k == 0 and n == 1:
	print(777, end=' ')
elif n // 2 > k or n == 1:
	print(-1)
	exit()
else:
	real = k - (n - 2) // 2
	k -= real
	print(real * 2, real, end=' ')
	r = real * 2 + 10
	while k > 0:
		print(r, r + 1, end=' ')
		k -= 1
		r += 2
	if n % 2 == 1:
		print(999999999, end=' ')
print()


import sys
(n, k) = list(map(int, input().split()))
if k < n // 2 or (n == 1 and k):
	print(-1)
	exit(0)
if n == 1:
	print(1)
	exit(0)
score = ((n ^ 1) - 2) // 2
gcd = k - score
ans1 = 200000000 - 200000000 % gcd
ans2 = ans1 + gcd
print(ans1, ans2, end=' ')
for i in range(1, n - 2 + 1):
	print(i, end=' ')


(n, k) = map(int, input().split())
if k * 2 + 1 < n:
	print(-1)
elif n == 1:
	if k == 0:
		print(1)
	else:
		print(-1)
else:
	output = []
	a = k - (n // 2 - 1)
	output.append(a)
	output.append(2 * a)
	output.extend([i for i in range(2 * a + 1, 2 * a + 1 + n - 2, 1)])
	print(' '.join([str(o) for o in output]))


(n, k) = map(int, input().split())
if n // 2 > k:
	print(-1)
elif n == 1 and k != 0:
	print(-1)
elif n == 1 and k == 0:
	print(1)
else:
	a = n // 2 - 1
	for i in range(1, a + 1):
		print(2 * i - 1, 2 * i, end=' ')
	print((k - a) * 3 + 4 * a - 4 * a % (k - a), 4 * a - 4 * a % (k - a) + (k - a) * 4, end=' ')
	if n % 2:
		print(998244353)


(m, k) = [int(x) for x in input().split()]
n = m
if m % 2 == 1:
	n -= 1
if m == 1:
	if k == 0:
		print(1)
	else:
		print(-1)
elif k < n // 2:
	print(-1)
else:
	x = k - (n // 2 - 1)
	ans = [str(x), str(2 * x)]
	i = 1
	while len(ans) < m:
		if i not in [x, 2 * x]:
			ans.append(str(i))
		i += 1
	print(' '.join(ans))


import sys
input = sys.stdin.readline
I = lambda : list(map(int, input().split()))
(n, k) = I()
if k < n // 2 or (n == 1 and k != 0):
	print(-1)
elif n == 1:
	print(1)
else:
	x = r = k - (n - 2) // 2
	while r <= x + n:
		r += x
	an = [r, x]
	for i in range(2, n):
		an.append(an[1] + i - 1)
	print(*an)