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, m, maxi, mini, cnt, ans, k, t[100001];
long long c1, c2, x, y;
string s, s2;
vector<int> a, b;
int main() {
  cin >> n >> k;
  if (k == 1) {
    for (int i = 1; i <= n; ++i) printf("%d ", i);
    return 0;
  }
  int l = 2;
  int r = n - 1;
  printf("%d %d ", l - 1, r + 1);
  --k;
  t[l - 1] = t[r + 1] = 1;
  for (int i = 2; i <= n; ++i) {
    if (k == 1) {
      if (i % 2 == 0) {
        for (int j = r; j > 0; --j)
          if (!t[j]) printf("%d ", j);
      } else {
        for (int j = l; j < n; ++j)
          if (!t[j]) printf("%d ", j);
      }
      return 0;
    }
    if (i & 1) {
      printf("%d ", r);
      t[r] = 1;
      --r;
    } else {
      printf("%d ", l);
      t[l] = 1;
      ++l;
    }
    --k;
  }
  return 0;
}
