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 n, k, v[100100];
int main() {
  scanf("%d %d", &n, &k);
  if (k == 1) {
    for (int i = 1; i <= n; i++) printf("%d ", i);
  } else {
    int a = 1, b = k + 1, p = k + 1, step = 0;
    while (p > 0) {
      if (step == 0) {
        v[p] = b;
        b--;
        step ^= 1;
      } else {
        v[p] = a;
        a++;
        step ^= 1;
      }
      p--;
    }
    for (int i = k + 1; i <= n; i++) v[i] = i;
    for (int i = 1; i <= n; i++) printf("%d ", v[i]);
  }
  return 0;
}
