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>
#pragma warning(disable : 4996)
using namespace std;
int n, k;
bool v[100005];
int main() {
  int i, l, r;
  scanf("%d%d", &n, &k);
  l = 1;
  r = n;
  memset(v, 0, sizeof(v));
  for (i = 1; i <= k; i++)
    if (i % 2 == 0) {
      printf("%d ", r);
      v[r] = true;
      r--;
    } else {
      printf("%d ", l);
      v[l] = true;
      l++;
    }
  if (k % 2 == 0) {
    for (i = r; i >= 1; i--)
      if (!v[i]) {
        printf("%d ", i);
      } else
        break;
  } else {
    for (i = l; i <= n; i++)
      if (!v[i]) {
        printf("%d ", i);
      } else
        break;
  }
  return 0;
}
