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 vet[123456];
using namespace std;
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  int vez = k;
  int ult = -100000000;
  vet[0] = 1;
  for (int i = 1; i < n; i++) {
    if (vez) {
      if (i % 2) {
        vet[i] = vet[i - 1] + vez;
      } else {
        vet[i] = vet[i - 1] - vez;
      }
      --vez;
    } else {
      if (ult == -100000000) {
        vet[i] = vet[1] + 1;
        ult = 2;
      } else
        vet[i] = vet[i - 1] + 1;
    }
  }
  for (int i = 0; i < n; i++) {
    printf("%d ", vet[i]);
  }
  puts("");
  return 0;
}
