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 INF = 0x3f3f3f3f;
const int N = 1e5 + 5;
int ans[N];
int main() {
  int n, k;
  while (scanf("%d%d", &n, &k) != EOF) {
    int t = 0;
    for (int i = k; i > 0; --i) {
      if ((k - i) & 1) {
        ans[i] = k - t;
        ++t;
      } else
        ans[i] = t + 1;
    }
    for (int i = k + 1; i <= n; ++i) ans[i] = i;
    for (int i = 1; i <= n; ++i) printf("%d%s", ans[i], i == n ? "\n" : " ");
  }
  return 0;
}
