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>
struct graw {
  long long x;
  long long y;
};
bool cmp(graw a, graw b) {
  if (a.x < b.x)
    return 0;
  else
    return 1;
}
using namespace std;
int main() {
  long long n, m, k;
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  cout << 1 << " ";
  long long v = 2;
  bool z = 0;
  for (long long i = 1; i < k; i++) {
    if (i % 2 != 0) {
      cout << n << " ";
      n--;
      z = 1;
    } else {
      cout << v << " ";
      v++;
      z = 0;
    }
  }
  if (z == 0) {
    for (long long i = v; i <= n; i++) {
      cout << i << " ";
    }
  } else {
    for (long long i = n; i >= v; i--) {
      cout << i << " ";
    }
  }
}
