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;
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return (a * (b / gcd(a, b))); }
int a[100010];
int main() {
  long long n, k, x = 1, t1, t2, tmp;
  cin >> n >> k;
  vector<long long> ans(n);
  t1 = 1;
  t2 = t1 + k;
  tmp = k;
  for (int i = 0; i < int(n); ++i) {
    if (i % 2 == 0) {
      a[t1] = 1;
      cout << t1++ << " ";
    } else {
      a[t2] = 1;
      cout << t2-- << " ";
    }
    if (tmp == 0) {
      for (int i = int(1); i < int(n + 1); ++i)
        if (!a[i]) cout << i << " ";
      break;
    } else
      tmp--;
  }
  return 0;
}
