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;
inline void zigzag(int x) {
  int l = x, h = N;
  for (int i = 0; i < N - x + 1; ++i) {
    if (i & 1)
      printf("%d ", h--);
    else
      printf("%d ", l++);
  }
}
int main(void) {
  scanf("%d%d", &N, &K);
  int n = N;
  for (int i = 0; i < N; ++i) {
    if (n - 1 == K) {
      zigzag(i + 1);
      break;
    }
    printf("%d ", i + 1);
    --n;
  }
  printf("\n");
  return 0;
}
