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;
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
const long long oo = (long long)1e9;
const double eps = 1e-9;
const long long mod = 1000000007;
int main() {
  long long n, k;
  cin >> n >> k;
  long long a[n + 5];
  a[0] = 1;
  for (int i = 1; i <= k; i++) {
    if (i % 2 == 1) {
      a[i] = a[i - 1] + (k - i + 1);
    } else {
      a[i] = a[i - 1] - (k - i + 1);
    }
  }
  for (int i = k + 1; i < n; i++) {
    a[i] = i + 1;
  }
  for (int i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
  return 0;
}
