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>
const int N = 100005;
int mark[N];
int main() {
  int n, k;
  while (scanf("%d%d", &n, &k) != EOF) {
    memset(mark, 0, sizeof(mark));
    int count = 0;
    int l = 1, r = n;
    int flag = 1;
    while (count < k) {
      if (flag) {
        printf("%d ", l);
        mark[l] = 1;
        l++;
        flag = 0;
      } else {
        printf("%d ", r);
        mark[r] = 1;
        r--;
        flag = 1;
      }
      count++;
    }
    if (flag) {
      for (int i = r; i >= 1; i--) {
        if (mark[i] == 0) printf("%d ", i);
      }
    } else {
      for (int i = l; i <= n; i++) {
        if (mark[i] == 0) printf("%d ", i);
      }
    }
    printf("\n");
  }
}
