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 n, k, A[100005], cnt;
int main() {
  scanf("%d%d", &n, &k);
  A[cnt = 1] = 1;
  for (int i = 2; i <= k; i++) A[++cnt] = i & 1 ? i + 1 >> 1 : n - (i - 1 >> 1);
  for (int i = cnt + 1; i <= n; i++)
    A[i] = cnt & 1 ? A[cnt] + i - cnt : A[cnt] - i + cnt;
  for (int i = 1; i <= n; i++) printf("%d ", A[i]);
}
