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 BUF_SIZE = 1 << 12;
char buf[BUF_SIZE], *buf_s = buf, *buf_t = buf + 1;
template <typename _n_>
void mian(_n_ &_x_) {
  while (*buf_s != '-' && !isdigit(*buf_s)) {
    buf_s++;
    if (buf_s == buf_t) {
      buf_s = buf;
      buf_t = buf + fread(buf, 1, BUF_SIZE, stdin);
    }
  };
  bool register _nega_ = false;
  if (*buf_s == '-') {
    _nega_ = true;
    {
      buf_s++;
      if (buf_s == buf_t) {
        buf_s = buf;
        buf_t = buf + fread(buf, 1, BUF_SIZE, stdin);
      }
    };
  }
  _x_ = 0;
  while (isdigit(*buf_s)) {
    _x_ = _x_ * 10 + *buf_s - '0';
    {
      buf_s++;
      if (buf_s == buf_t) {
        buf_s = buf;
        buf_t = buf + fread(buf, 1, BUF_SIZE, stdin);
      }
    };
  }
  if (_nega_) _x_ = -_x_;
}
const int kato = 1e5 + 10;
template <typename _n_>
bool cmax(_n_ &a, const _n_ &b) {
  return a < b ? a = b, 1 : 0;
}
template <typename _n_>
bool cmin(_n_ &a, const _n_ &b) {
  return a > b ? a = b, 1 : 0;
}
int n, k, a[kato];
inline int Ame_() {
  mian(n), mian(k);
  int l = 1, r = n;
  for (int i = 1; i <= n; i++) {
    if (i & 1)
      a[i] = l, l++;
    else
      a[i] = r, r--;
  }
  for (int i = k + 1; i <= n; i++) {
    if (k & 1)
      a[i] = a[i - 1] + 1;
    else
      a[i] = a[i - 1] - 1;
  }
  for (int i = 1; i <= n; i++) printf("%d ", a[i]);
  return ~~(0 ^ 0 ^ 0);
}
int Ame__ = Ame_();
int main() { ; }
