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 main() {
  int n, k;
  cin >> n >> k;
  vector<int> v(n);
  int val = 1;
  for (int i = 0; i < n; i++) {
    v[i] = val;
    if (i + 1 < n) {
      v[i + 1] = n - val + 1;
      val++;
      i++;
    }
  }
  int i;
  for (i = 0; i < k; i++) {
    cout << v[i] << " ";
  }
  int mn = 1e9, mx = 0;
  for (int j = i; j < n; j++) {
    if (v[j] > mx) mx = v[j];
    if (v[j] < mn) mn = v[j];
  }
  if ((k - 1) % 2 == 0) {
    for (i; i < n; i++) cout << mn++ << " ";
  } else {
    for (i; i < n; i++) cout << mx-- << " ";
  }
}
