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 gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
double dist(long long a, long long b, long long c, long long d) {
  return sqrt((a - c) * (a - c) + (b - d) * (b - d));
}
int main() {
  int i, j, a[100005], k, m, n, x, y, z;
  cin >> n >> k;
  int diff = k;
  i = 0;
  a[0] = 1;
  int flag = 1;
  i++;
  while (diff > 0) {
    if (flag)
      a[i] = a[i - 1] + diff;
    else
      a[i] = a[i - 1] - diff;
    i++;
    flag = flag ^ 1;
    diff--;
  }
  diff = 2 + k;
  while (i < n) {
    a[i] = i + 1;
    i++;
  }
  for (int i = 0; i < (n); ++i) cout << a[i] << " ";
  return 0;
}
