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;
bool u[100010];
int n, k, x;
int main() {
  cin >> n >> k;
  if (k == 1) {
    for (int i = 1; i <= n; i++) printf("%d ", i);
    return 0;
  }
  memset(u, 0, sizeof(u));
  x = 1;
  u[1] = 1;
  cout << 1;
  for (int i = k; i >= 1; i--) {
    if (x + i <= k + 1 && !u[x + i])
      printf(" %d", x + i), x += i, u[x] = 1;
    else
      printf(" %d", x - i), x -= i, u[x] = 1;
  }
  for (int i = k + 2; i <= n; i++) printf(" %d", i);
  return 0;
}
