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 comment(linker, "/STACK:1000000000")
using namespace std;
const int N = 100001;
int n, k;
int ans[N];
int main() {
  scanf("%d%d", &n, &k);
  ans[0] = 1;
  int l = 2, r = n, pos = 1;
  int it = 1;
  while (k > 1) {
    if (it == 1)
      ans[pos++] = r--;
    else
      ans[pos++] = l++;
    k--;
    it ^= 1;
  }
  if (it == 1)
    for (int i = pos; i < n; ++i) ans[i] = l++;
  else
    for (int i = pos; i < n; ++i) ans[i] = r--;
  for (int i = 0; i < n; ++i) printf("%d ", ans[i]);
  return 0;
}
