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[1000005], flag[1000005];
int n, k;
int main() {
  cin >> n >> k;
  a[1] = 1;
  int l = 2, r = n;
  while (l <= r) {
    int mid = (l + r) >> 1;
    a[2] = mid;
    int x = 2, y = mid - 1;
    int m = 2;
    for (; x < y; ++x, --y) a[++m] = x, a[++m] = y;
    if (x == y) a[++m] = x;
    for (int i = mid + 1; i <= n; ++i) a[++m] = i;
    for (int i = 1; i <= n; ++i) flag[i] = 0;
    int tot = 0;
    for (int i = 1; i < n; ++i)
      if (!flag[abs(a[i] - a[i + 1])]) flag[abs(a[i] - a[i + 1])] = 1, ++tot;
    if (k == tot) {
      l = mid;
      break;
    }
    if (k < tot)
      r = mid - 1;
    else
      l = mid + 1;
  }
  for (int i = 1; i < n; ++i) printf("%d ", a[i]);
  printf("%d\n", a[n]);
}
