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;
int ara[100005];
int vis[100005];
int main() {
  int n, k, m = 1;
  cin >> n >> k;
  if (k % 2 == 0) {
    for (int i = 1; i < k; i++) {
      if (i % 2 != 0) {
        vis[m] = 1;
        cout << m++;
      } else {
        vis[n] = 1;
        cout << n--;
      }
      cout << " ";
    }
    for (int i = n; i >= 1; i--) {
      if (vis[i] != 1) {
        cout << i << " ";
      }
    }
  } else {
    for (int i = 1; i <= k; i++) {
      if (i % 2 != 0) {
        vis[m] = 1;
        cout << m++;
      } else {
        vis[n] = 1;
        cout << n--;
      }
      cout << " ";
    }
    for (int i = 1; i <= n; i++) {
      if (vis[i] != 1) {
        cout << i << " ";
      }
    }
  }
}
