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 int N = 1e5 + 11;
int main() {
  int n, k;
  while (scanf("%d %d", &n, &k) == 2) {
    int i = 1, j = n;
    while (i + k < n) {
      printf("%d ", i);
      ++i;
    }
    while (i <= j) {
      if (i == j) {
        printf("%d", i);
        break;
      } else {
        printf("%d %d", i, j);
        ++i, --j;
        if (i > j) break;
        printf(" ");
      }
    }
    printf("\n");
  }
}
