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 int maxnum = 1e5 + 100;
int a[maxnum];
int main() {
  int n, k;
  cin >> n >> k;
  int before = 1;
  int cha = k;
  int now;
  int hehe = 1;
  a[1] = 1;
  for (int i = 1; i <= n; ++i) {
    if (i == 1)
      cout << "1";
    else {
      int temp1 = before + cha;
      int temp2 = before - cha;
      if (temp2 > 0) {
        if (hehe && temp1 <= n && a[temp1] == 0) {
          a[temp1] = 1;
          cout << " " << temp1;
          before = temp1;
          hehe = 0;
        } else {
          cout << " " << temp2;
          before = temp2;
          a[temp2] = 1;
          hehe = 1;
        }
      } else {
        cout << " " << temp1;
        before = temp1;
        a[temp1] = 1;
        hehe = 0;
      }
      --cha;
      if (cha == 0) {
        break;
      }
    }
  }
  for (int i = 1; i <= n; ++i) {
    if (a[i] == 0) cout << " " << i;
  }
  cout << endl;
}
