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>
int main() {
  int n, i, k, a[100002], ok, sum;
  while (scanf("%d %d", &n, &k) != EOF) {
    ok = 0;
    a[1] = 1;
    printf("1");
    sum = n - 1;
    for (i = 2; i <= n; i++) {
      if (k != 1) {
        if (ok == 0) {
          a[i] = a[i - 1] + sum;
          printf(" %d", a[i]);
        } else {
          a[i] = a[i - 1] - sum;
          printf(" %d", a[i]);
        }
        ok = 1 - ok;
        sum--;
        k--;
      } else {
        if (ok == 1) {
          a[i] = a[i - 1] - 1;
          printf(" %d", a[i]);
        } else {
          a[i] = a[i - 1] + 1;
          printf(" %d", a[i]);
        }
      }
    }
    printf("\n");
  }
}
