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;
using ll = long long int;
using dl = double;
const int N = 2e5 + 10;
ll aarray[200000 + 10];
ll magic[101][101];
vector<ll> primes;
bool prime[1000001];
int main() {
  ios_base::sync_with_stdio(false);
  string str;
  ll i, j, n, m, k, t;
  cin >> n >> k;
  memset(prime, true, sizeof(prime));
  vector<ll> ans;
  ll f, l;
  f = 1, l = n;
  for (i = 0; i < k; i++) {
    if ((i & 1) == 0) {
      cout << f << " ";
      f++;
    } else {
      cout << l << " ";
      l--;
    }
  }
  for (i = k; i < n; i++) {
    if ((k & 1)) {
      cout << f << " ";
      f++;
    } else {
      cout << l << " ";
      l--;
    }
  }
  cout << endl;
  return 0;
}
