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;
bool used[100010];
int main() {
  int n, k;
  cin >> n >> k;
  memset(used, false, sizeof(false));
  if (k != 1) {
    int saveK = k;
    cout << 1 << " ";
    int prv = 1;
    used[prv];
    int saveN = n;
    bool found = false;
    for (int i = 1; i < saveN && !found; i++) {
      if (k == 1) {
        n--;
        cout << n << " ";
      } else {
        if (i % 2 == 1) {
          cout << n << " ";
          n--;
          k--;
          if (k == 1) {
            while (n > prv) {
              cout << n << " ";
              n--;
            }
            found = true;
          }
        } else {
          prv++;
          cout << prv << " ";
          k--;
          if (k == 1) {
            while (prv < n) {
              prv++;
              cout << prv << " ";
            }
            found = true;
          }
        }
      }
    }
  } else {
    for (int i = 0; i < n; i++) cout << i + 1 << " ";
  }
  cout << endl;
  return 0;
}
