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 main() {
  long long n, k, a = 1, b, frq[100005];
  scanf("%lld %lld", &n, &k);
  memset(frq, 0, sizeof(frq));
  printf("%lld ", a);
  frq[a]++;
  long long chk = 1;
  while (k) {
    if (chk % 2 != 0) {
      printf("%lld ", a + k);
      a = a + k;
      k--;
      frq[a]++;
    } else {
      printf("%lld ", a - k);
      a = a - k;
      k--;
      frq[a]++;
    }
    chk++;
  }
  for (long long i = 1; i <= n; i++) {
    if (!frq[i]) printf("%lld ", i);
  }
  printf("\n");
  return (0);
}
