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 n, k;
int main() {
  while (~scanf("%d %d", &n, &k)) {
    int cnt = k - 1;
    int i = 2, j = n;
    bool put = false;
    bool have_put = false;
    printf("1");
    while (k - 1 > 0) {
      if (put) {
        printf(" %d", i);
        put = false;
        i++;
      } else {
        printf(" %d", j);
        put = true;
        j--;
      }
      have_put = true;
      k--;
    }
    if (i <= j) {
      if (put) {
        while (j >= i) {
          printf(" %d", j--);
        }
      } else {
        while (i <= j) {
          printf(" %d", i++);
        }
      }
    }
    printf("\n");
  }
  return 0;
}
