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:32000000")
using namespace std;
long long n, m, k, d, w;
int log2n(int x) {
  int res = 1;
  while ((1 << res) <= x) res++;
  return res - 1;
}
int main() {
  int n, k;
  cin >> n >> k;
  int i;
  int ma = n + 1, mi = 0;
  int last;
  for (i = 1; i <= k; i++) {
    if (i % 2 == 0) {
      cout << i / 2 << " ";
      mi = i / 2;
      last = mi;
    } else {
      cout << n - i / 2 << " ";
      ma = n - i / 2;
      last = ma;
    }
  }
  i--;
  if (i % 2 == 0) {
    for (int j = mi + 1; j < ma; j++) cout << j << " ";
  } else {
    for (int j = ma - 1; j > mi; j--) cout << j << " ";
  }
  return 0;
}
