Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
#include <bits/stdc++.h>
using namespace std;
const double error = 1e-15;
const double pi = 2 * acos(0);
const int maxn = (int)1e5 + 10;
const int mod = (int)1e9;
int A[100005];
int main() {
  long n, k, i, j, pr, flg = 0;
  cin >> n >> k;
  A[1] = 1;
  pr = 1;
  cout << "1 ";
  while (k > 0) {
    if (flg == 0) {
      pr = pr + k;
      A[pr] = 1;
      flg = 1;
    } else {
      pr = abs(k - pr);
      A[pr] = 1;
      flg = 0;
    }
    cout << pr << " ";
    k--;
  }
  for (i = 1; i <= n; i++)
    if (A[i] == 0) cout << i << " ";
  return 0;
}
