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;
long long power(long long b, long long e) {
  long long p = 1;
  while (e > 0) {
    if (e & 1) {
      p = (p * b) % 1000000007;
    }
    e = e >> 1;
    b = (b * b) % 1000000007;
  }
  return p;
}
int main() {
  long long n, i, t, x = 0, l, k, m;
  scanf("%lld", &n);
  scanf("%lld", &k);
  m = k + 1;
  for (i = x = 1; x < k + 2; x++) {
    if (x % 2) {
      printf("%lld ", i++);
    } else
      printf("%lld ", m--);
  }
  for (i = x; i <= n; i++) printf("%lld ", i);
  return 0;
}
