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() {
  long long n, m, i, j, k;
  vector<long long> vec;
  cin >> n >> m;
  for (int i = 1; i < n + 1; i++) {
    vec.push_back(i);
  }
  if (n == m)
    cout << -1 << endl;
  else {
    k = n - m;
    if (k % 2 == 0) {
      for (i = 0; i < n - m; i += 2) {
        swap(vec[i], vec[i + 1]);
      }
    } else {
      for (i = 1; i < n - m - 1; i += 2) {
        swap(vec[i], vec[i + 1]);
      }
    }
    for (i = 0; i < n; i++) cout << vec[i] << " ";
    cout << endl;
  }
}