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 a[100009];
int n, k;
int vis[100009];
int main() {
  while (scanf("%d %d", &n, &k) == 2) {
    memset(vis, 0, sizeof(vis));
    int t = k;
    a[0] = 1;
    vis[1] = 1;
    int f = 1;
    int ok = 0;
    int i = 1;
    while (t > 0) {
      int temp = a[i - 1] + (f * t);
      if (!vis[temp] && temp != 0) {
        a[i] = temp;
        vis[temp] = 1;
      } else {
        temp = a[i - 1] - (f * t);
        vis[temp] = 1;
        a[i] = temp;
      }
      f = -f;
      i++;
      t--;
    }
    for (int j = 1; j < 100009; j++) {
      if (!vis[j]) a[i++] = j;
      if (i >= n) break;
    }
    printf("%d", a[0]);
    for (int i = 1; i < n; i++) printf(" %d", a[i]);
    printf("\n");
  }
  return 0;
}
