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 int n, k, v, m, ans, sum, sum1, l, r, i, j, mx,
    mn = 1222999000, c, z, x, y, a[111111], d[111111], t[111111];
vector<int> b[111111];
string s, sos, ss;
char ch[111111], chel;
bool used[111111];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  x = 1;
  y = k;
  for (i = 1; i <= k + 1; i++) {
    cout << x << " ";
    if (c == 0) {
      x += y;
      c = 1;
    } else {
      x -= y;
      c = 0;
    }
    y--;
  }
  for (i = 1; i <= n - k - 1; i++) {
    cout << i + k + 1 << " ";
  }
  return 0;
}
