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>
int setbit(int N, int pos) { return N = N | (1 << pos); }
int resetbit(int N, int pos) { return N = N & ~(1 << pos); }
bool checkbit(int N, int pos) { return (bool)(N & 1 << pos); }
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  int cnt = n;
  int i = 1;
  for (; i <= n; i++) {
    if (i == 1)
      cout << 1;
    else
      cout << " " << i;
    if (n - i == k) break;
  }
  cnt -= i;
  bool isg = false;
  cout << " " << n;
  i = n;
  cnt--;
  k--;
  while (cnt--) {
    if (isg) {
      cout << " " << i + k;
      i = i + k;
      k--;
      isg = false;
    } else {
      i = i - k;
      cout << " " << i;
      k--;
      isg = true;
    }
  }
  return 0;
}
