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 double pi = 3.14159265358979323846;
long long ten[19] = {1,
                     10,
                     100,
                     1000,
                     10000,
                     100000,
                     1000000,
                     10000000,
                     100000000,
                     1000000000,
                     10000000000,
                     100000000000,
                     1000000000000,
                     10000000000000,
                     100000000000000,
                     1000000000000000,
                     10000000000000000,
                     100000000000000000,
                     1000000000000000000};
inline void eatline() {
  while (getchar() != '\n')
    ;
}
using namespace std;
const int S = 100000;
int main() {
  int n, k;
  cin >> n >> k;
  int l = 1, r = k + 1, cnt = 0;
  for (; l < r; l++, r--) {
    cout << ' ' << l << ' ' << r;
    cnt += 2;
  }
  if (k % 2 == 0) {
    cout << ' ' << r;
    cnt++;
  }
  while (cnt < n) {
    cout << ' ' << ++cnt;
  }
  cout << endl;
}
