Problem: 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.

Solution (in PYTHON3):

Solution:
from math import ceil
from math import floor	
from math import sqrt
from math import log

def mod_expo(n, p, m):
	"""find (n^p)%m"""
	result = 1
	while p != 0:
		if p%2 == 1:
			result = (result * n)%m
		p //= 2
		n = (n * n)%m
	return result
	
def find_least_diff(n):
	A = 2*(pow(2, n/2-1) - 1) 
	B = -pow(2, n/2)
	return int(abs(B - A))
	
def find_ways(n):
	return((n-1)//2)

		
def count_digits(n):
	m = 9
	count=n
	while True:
		if n >= m:
			count += n-m
		else:
			break
		m = str(m)
		m += "9"
		m = int(m)
	return count
	
def kth_bit_set(n, k):
	return (n & (1 << (k-1)))	

def sum_is_zero(n, arr):
	for i in range(pow(2, n)):
		angle_sum = 0
		for j in range(n):
			if kth_bit_set(i, j+1):
				angle_sum += arr[j]
			else:
				 angle_sum -= arr[j]
		if angle_sum%360 == 0:
			return True
	return False
	
def get_board(n, m, mat):
	for i in range(n):
		for j in range(m):
	
			print(i, j)
			if mat[i][j] == '.':
				if (j > 0 and mat[i][j-1] != 'B') and (i > 0 and mat[i-1][j] != 'B'):
					mat[i][j] = 'B'
				else:
					mat[i][j] = 'W'
	for i in range(n):
		for j in range(m):
			print(mat[i][j])
			
def check_and_print_pyth_triplets(n):
	if n <= 2:
		print(-1)
	elif n%2 == 0:
		temp = n*n
		m = temp/4 - 1
		k = temp/4 + 1
		print(str(m), str(k))
	else:
		temp = n*n
		m = (temp-1)/2
		k = (temp + 1)/2
		print(str(m), str(k))

def can_equalize(n, arr, b):
	a = 0
	g = 0
	result = ""
	for i in range(n):
		if (a + arr[i]) - g <= 500:
			a += arr[i]
			result += "A"
		else:
			g += b[i]
			result += "G"
	if (abs(a-g) <= 500):
		return result
	return "-1"
	
def is_square(a1, b1, a2, b2):
	if a1 == a2 and (b1 + b2 == a1):
		return True
	elif a1 == b2 and (b1 + a2 == a1):
		return True
	elif b1 == a2 and (a1 + b2 == b1):
		return True
	elif b1 == b2 and (a1 + a2 == b1):
		return True
		
	return False

def find_given_gcd(n, k):
	if n == 1:
		if k == 0:
			return [2]
		return [-1]
	if k >= n//2:
		answers = []
		x = k - floor((n-2)/2)
		answers.append(x)
		answers.append(2*x)
		current = 2*x + 1
		count = 2
		while count < n:
			answers.append(current)
			count += 1
			current += 1
		return answers
	return [-1]
def there_is_a_way(n, pipes):
	row=0
	for c in range(0, n):
		if pipes[c][row] <= 2:
			continue
		else:
			nxt_row = (row + 1)%2
			if pipes[c][nxt_row] > 2:
				row = nxt_row
			else:
				return false
	return (row == 1)
				
	
def contest_function(n, arr):
	count=1
	i=n-1
	mx=0
	while i > 0:
		if arr[i] <= 2*arr[i-1]:
			count += 1
		else:
			mx = max(mx, count)
			count=1
		i -= 1
	return mx

def fun(y):
	return (1/3)*((1/sqrt(1 +y*y) + 1/sqrt(25 +y*y)) +
		4*(1/sqrt(1 +4*y*y) + 1/sqrt(1 +16*y*y)) +
		2*1/sqrt(1 +9*y*y))

t=1
#t=int(input())
while t:
	t = t - 1
	count=0
	# n, ox, oy = map(int, input().split())
	n, k = map(int, input().split())
	# text = input()
	# n = int(input())
	# above = list(map(int, input().strip().split()))[:n]
	# above = input()
	# below = input()
	arr = []
	b = []
	
	#a1, b1 = map(int, input().split())
	#a2, b2 = map(int, input().split())
	
	# print(a + g)
	
	# print(can_equalize(n, arr, b))
	#if is_square(a1, b1, a2, b2):
	# 	print("YES")
	#else:
	#	print("NO")
	answers = find_given_gcd(n, k)
	print(*answers, sep=' ')
	#print(contest_function(n, arr))