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>
using namespace std;
namespace patch {
template <typename T>
std::string to_string(const T& n) {
  std::ostringstream stm;
  stm << n;
  return stm.str();
}
}  // namespace patch
const long double PI = 3.14159265358979323846;
struct Point {
  double x, y;
};
long long gcd(long long a, long long b) { return a == 0 ? b : gcd(b % a, a); }
bool isAPrime(long long m) {
  for (long long p = 2; p * p <= m; p++) {
    if (m % p == 0) {
      return false;
    }
  }
  return true;
}
long long mdf = 1e+9 + 7;
long long binpow(long long a, long long n) {
  if (n == 0) return 1;
  if (n % 2 == 1)
    return (binpow(a, n - 1) * a) % mdf;
  else {
    long long b = binpow(a, n / 2) % mdf;
    return (b * b) % mdf;
  }
}
int count_setbits(int N) {
  int cnt = 0;
  while (N > 0) {
    cnt += (N & 1);
    N = N >> 1;
  }
  return cnt;
}
long long phi(long long n) {
  long long result = n;
  for (long long i = 2; i * i <= n; ++i)
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      result -= result / i;
    }
  if (n > 1) result -= result / n;
  return result;
}
bool compare(pair<int, long long> a, pair<int, long long> b) {
  return a.second < b.second;
}
int mergethem(vector<int>& a, int l, int m, int r) {
  int Inv = 0;
  vector<int> buff(r - l + 1);
  int pos1 = l, pos2 = m + 1, posB = 0;
  while (pos1 <= m && pos2 <= r) {
    if (a[pos1] < a[pos2]) {
      buff[posB++] = a[pos1++];
    } else {
      Inv += m - pos1 + 1;
      buff[posB++] = a[pos2++];
    }
  }
  while (pos1 <= m) buff[posB++] = a[pos1++];
  while (pos2 <= r) buff[posB++] = a[pos2++];
  copy(buff.begin(), buff.end(), a.begin() + l);
  return Inv;
}
int mergesort(vector<int>& a, int l, int r) {
  int curInv = 0;
  if (l == r) return curInv;
  int m = (l + r) / 2;
  curInv += mergesort(a, l, m);
  curInv += mergesort(a, m + 1, r);
  curInv += mergethem(a, l, m, r);
  return curInv;
}
void solve() {
  int n, k;
  cin >> n >> k;
  bool was = n % 2;
  if (n % 2) n--;
  if (n / 2 > k || (n == 0 && k > 0)) {
    cout << -1;
    return;
  }
  int last = 1e9;
  for (int i = 0; i < n / 2 - 1; i++) {
    cout << last << " " << last - 1 << " ";
    last -= 2;
  }
  if (n / 2 >= 1)
    cout << k - (n / 2 - 1) << " " << 2 * (k - (n / 2 - 1)) << " ";
  if (was) cout << last;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int q = 1;
  while (q--) solve();
  return 0;
}