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;
const int N = 1e5 + 5;
bool vis[N];
int n, k, a[N];
inline int read() {
  int x, f = 1;
  char ch;
  while (!(isdigit(ch = getchar()))) ch == '-' ? f = -1 : f;
  x = ch ^ 48;
  while ((isdigit(ch = getchar()))) x = (x << 1) + (x << 3) + (ch ^ 48);
  return f * x;
}
int main() {
  n = read();
  k = read();
  for (int i = 1; i <= k; i++) {
    if (i & 1) {
      a[i] = (i + 1) >> 1;
      vis[(i + 1) >> 1] = 1;
    } else {
      a[i] = n - (i >> 1) + 1;
      vis[n - (i >> 1) + 1] = 1;
    }
  }
  if (k & 1) {
    int l = a[k];
    while (l <= n) {
      if (!vis[l]) a[++k] = l;
      l++;
    }
  } else {
    int l = a[k];
    while (l) {
      if (!vis[l]) a[++k] = l;
      l--;
    }
  }
  for (int i = 1; i <= n; i++) printf("%d ", a[i]);
  return 0;
}
