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;
const int N = 200006;
const int MAX = 1000 * 100 + 1;
const long long INF = 1e18;
const int MOD = 1000 * 1000 * 1000 + 7;
const int dx[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
vector<long long> v[N], v1, v2;
long long a[N], b[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, m;
  cin >> n >> m;
  for (int i = (1); i <= (n); i++) a[i] = i;
  long long x = n - m - 1;
  x = x / 2;
  long long y = m, z = 2;
  while (y) {
    if (z % 2 == 0) {
      a[x + z] = a[x + z - 1] + y;
    } else
      a[x + z] = a[x + z - 1] - y;
    z++;
    y--;
  }
  for (int i = (1); i <= (n); i++) cout << a[i] << " ";
}
