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;
  int flag = k, arr[100005];
  bool temp[100005];
  memset(temp, false, sizeof temp);
  arr[1] = 1;
  temp[1] = true;
  for (int i = 2; i <= k; i++) {
    if (i % 2 == 0) {
      arr[i] = arr[i - 1] + flag;
      temp[arr[i]] = true;
    } else {
      arr[i] = arr[i - 1] - flag;
      temp[arr[i]] = true;
    }
    flag--;
  }
  int x = k + 1;
  for (int i = 1; i <= n; i++) {
    if (temp[i] == false) {
      arr[x] = i;
      x++;
    }
  }
  for (int i = 1; i <= n; i++) {
    cout << arr[i] << " ";
  }
  return 0;
}
