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 main() {
  int i, j, k, k1, n, tmp;
  while (scanf("%d%d", &n, &k) == 2) {
    bool flag = 1;
    k1 = k;
    tmp = 1;
    printf("1");
    while (k1 > 0) {
      if (flag)
        tmp += k1;
      else
        tmp -= k1;
      printf(" %d", tmp);
      flag = !flag;
      k1--;
    }
    for (i = k + 2; i <= n; i++) {
      printf(" %d", i);
    }
    printf("\n");
  }
}
