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 CPP):

Solution:
#include <bits/stdc++.h>
const long long INF = (long long)1e7 + 1;
const long long mod = (long long)998244353;
const long long hell = (long long)1000000007;
using namespace std;
long long int power(long long int x, long long int y, long long int md) {
  long long int res = 1;
  while (y > 0) {
    if (y % 2) res = (x % md * res % md) % md;
    x = (x % md * x % md) % md;
    y = y / 2;
  }
  return res;
}
long long int modinv(long long int x) { return power(x, hell - 2, hell); }
void solve();
void fastIO() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int main() {
  fastIO();
  int test;
  test = 1;
  while (test--) solve();
}
long long int pw(long long int k, long long int x);
long long int gcd(long long int x, long long int y);
void solve() {
  int n, k;
  cin >> n >> k;
  if (k < n / 2) {
    cout << -1;
    return;
  }
  if (n == 1 and k == 0) {
    cout << 1;
    return;
  }
  if (n == 1) {
    cout << -1;
    return;
  }
  int x = n / 2;
  x--;
  k -= x;
  if (k == 0) k = 1;
  cout << k << " " << 2 * k << " ";
  for (int i = 1; i <= n - 2; i++) {
    cout << 2 * k + i << " ";
  }
}
long long int gcd(long long int a, long long int b) {
  while (b != 0) {
    long long int t = b;
    b = a % t;
    a = t;
  }
  return a;
}
long long int pw(long long int k, long long int x) {
  if (x == 0) return 1;
  if (x & 1)
    return ((pw(k, x - 1)) * k);
  else
    return ((pw(k, x / 2)) * (pw(k, x / 2)));
}