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 n, i, k, j, a[100001];
int main() {
  cin >> n >> k;
  if (k == 1)
    for (i = 1; i <= n; i++) cout << i << " ";
  else {
    if (k % 2 == 0) {
      j = n;
      for (i = 0; i < k; i += 2) {
        a[i] = j;
        j--;
      }
      j = 1;
      for (i = 1; i < k; i += 2) {
        a[i] = j;
        j++;
      }
      for (i = i - 1; i < n; i++) {
        a[i] = j;
        j++;
      }
    } else {
      j = n;
      for (i = 1; i < k; i += 2) {
        a[i] = j;
        j--;
      }
      j = 1;
      for (i = 0; i < k; i += 2) {
        a[i] = j;
        j++;
      }
      for (i--; i < n; i++) {
        a[i] = j;
        j++;
      }
    }
    for (i = 0; i < n; i++) cout << a[i] << " ";
  }
}
