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;
int a[100002];
int main() {
  scanf("%d %d", &N, &K);
  if (K == 1) {
    for (int i = 1; i <= N; i++) printf("%d ", i);
    printf("\n");
    exit(0);
  }
  int l = 1;
  int r = N;
  for (int i = 1; i <= K; i++) {
    if (i % 2 == 0)
      a[i] = r--;
    else
      a[i] = l++;
  }
  if (K % 2 == 1) {
    for (int i = K + 1; i <= N; i++) {
      a[i] = l++;
    }
  } else {
    for (int i = K + 1; i <= N; i++) {
      a[i] = r--;
    }
  }
  for (int i = 1; i <= N; i++) printf("%d ", a[i]);
  printf("\n");
  return 0;
}
