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 gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long cnt1, cnt2, x, y;
bool f(long long v) { return v - v / x >= cnt1; }
bool f1(long long v) { return v - v / y >= cnt2; }
int main() {
  int n, k, l, r;
  cin >> n >> k;
  l = 1;
  r = n;
  while (r - l + 1 != n - k) {
    cout << l << " ";
    l++;
    if (r - l + 1 != n - k) {
      cout << r << " ";
      r--;
    } else {
      for (int i = l; i <= r; i++) cout << i << " ";
      return 0;
    }
  }
  for (int i = r; i >= l; i--) cout << i << " ";
}
