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;
long long int modpow(long long int a, long long int n, long long int temp) {
  long long int res = 1, y = a;
  while (n > 0) {
    if (n & 1) res = (res * y) % temp;
    y = (y * y) % temp;
    n /= 2;
  }
  return res % temp;
}
long long int gcd(long long int a, long long int b) {
  if (a == 0)
    return (b);
  else
    return (gcd(b % a, a));
}
int main() {
  std::ios_base::sync_with_stdio(false);
  int j, k, n, l = 0, i;
  cin >> n >> k;
  int r = n + 1;
  vector<int> a(n);
  for (i = 0; i < k; i++) {
    if (!(i & 1))
      a[i] = ++l;
    else
      a[i] = --r;
  }
  for (i = k; i <= n - 1; i++)
    if (a[k - 1] == l)
      a[i] = a[i - 1] + 1;
    else
      a[i] = a[i - 1] - 1;
  for (i = 0; i < n; i++) cout << a[i] << " ";
  return 0;
}
