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;
void print(int x) {
  int i = 1, j = x, k = 0, now = 0;
  for (k = 0; k < x; k++) {
    if (now == 0) {
      printf("%d ", i);
      i++;
      now = 1;
    } else {
      printf("%d ", j);
      j--;
      now = 0;
    }
  }
  return;
}
int main() {
  int n, k, i;
  cin >> n >> k;
  if (n == (k + 1)) {
    print(n);
    return 0;
  } else {
    print(k + 1);
    for (i = k + 2; i <= n; i++) printf("%d ", i);
  }
  printf("\n");
  return 0;
}
