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 getint() {
  int x = 0, tmp = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') c = getchar(), tmp = -1;
  while (c >= '0' && c <= '9') x *= 10, x += (c - '0'), c = getchar();
  return x * tmp;
}
int n, k;
void init() {
  n = getint();
  k = getint();
}
void solve() {
  for (int i = n; i > k + 1; i--) printf("%d ", i);
  printf("%d ", k + 1);
  int l = 1, r = k;
  for (int i = 1; i <= k; i++)
    if (i & 1) {
      printf("%d ", l);
      l++;
    } else {
      printf("%d ", r);
      r--;
    }
}
int main() {
  init();
  solve();
}
