Problem: Levko loves permutations very much. A permutation of length n is a sequence of distinct positive integers, each is at most n.

Let’s assume that value gcd(a, b) shows the greatest common divisor of numbers a and b. Levko assumes that element pi of permutation p1, p2, ... , pn is good if gcd(i, pi) > 1. Levko considers a permutation beautiful, if it has exactly k good elements. Unfortunately, he doesn’t know any beautiful permutation. Your task is to help him to find at least one of them.

Input

The single line contains two integers n and k (1 ≤ n ≤ 105, 0 ≤ k ≤ n).

Output

In a single line print either any beautiful permutation or -1, if such permutation doesn’t exist.

If there are multiple suitable permutations, you are allowed to print any of them.

Examples

Input

4 2


Output

2 4 3 1

Input

1 1


Output

-1

Note

In the first sample elements 4 and 3 are good because gcd(2, 4) = 2 > 1 and gcd(3, 3) = 3 > 1. Elements 2 and 1 are not good because gcd(1, 2) = 1 and gcd(4, 1) = 1. As there are exactly 2 good elements, the permutation is beautiful.

The second sample has no beautiful permutations.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  if ((n == 1 && k != 0) || k == n)
    cout << -1;
  else {
    if (k != n - 1 && (n - k - 1) % 2 == 0) {
      cout << 1 << " ";
      int i;
      for (i = 2; i <= k + 1; i++) {
        cout << i << " ";
      }
      for (int j = i; j <= n; j += 2) {
        cout << j + 1 << " " << j << " ";
      }
    } else {
      if ((n - k - 1) % 2 != 0) {
        int i;
        cout << n << " ";
        for (i = 2; i <= k + 1; i++) {
          cout << i << " ";
        }
        for (int j = i; j < n; j += 2) {
          cout << j + 1 << " " << j << " ";
        }
        cout << 1;
      } else {
        for (int i = 1; i <= n; i++) cout << i << " ";
      }
    }
  }
  return 0;
}