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;
const long long mod = 1e9 + 1;
const double eps = 1e-6;
int a[103040];
int main() {
  int n, k, flag = 2, s = 1;
  cin >> n >> k;
  a[1] = 1;
  while (k) {
    a[flag] = a[flag - 1] + s * k;
    s = -s;
    k--;
    flag++;
  }
  for (int i = flag; i < n + 1; i++) {
    a[i] = i;
  }
  for (int i = 1; i < n + 1; i++) {
    printf("%d ", a[i]);
  }
  return 0;
}
