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 n, k;
int a[1234567];
void swap(int i, int j) {
  int x = a[i];
  a[i] = a[j];
  a[j] = x;
}
int main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; i++) {
    a[i] = i;
  }
  if (k != 1) {
    k--;
    int ende = n;
    int p = 1;
    int maxx = n;
    for (int i = 1; i <= n; i++) {
      a[i] = (1 << 30);
    }
    for (int i = 1; i <= n; i++) {
      if (a[i] == (1 << 30)) {
        a[i] = p;
        p++;
        if (i % 2 == 0 && k > 0) {
          a[i] = maxx;
          ende = i;
          p--;
          k -= 2;
          maxx--;
        }
      }
    }
    if (k < 0) {
      for (int i = ende; i < n; i++) {
        if (abs(a[i + 1] - a[i]) == 1) {
          break;
        } else {
          swap(i, i + 1);
        }
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    cout << a[i] << " ";
  }
  return 0;
}
