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>
const int MOD = 1e9 + 7;
const long long int INF = 2e18;
const int mxn = 2e9 + 9;
const int mxd = 2e5 + 5;
const int mxa = 1e5 + 5;
int64_t gcd(int64_t a, int64_t b) {
  if (b == 0LL) return a;
  return gcd(b, a % b);
}
int64_t lcm(int64_t a, int64_t b) { return (a / gcd(a, b) * b); }
using namespace std;
void Run_Case() {
  int n, k;
  cin >> n >> k;
  int l = 1, r = n;
  for (int i = 0; i < k; i++) {
    if (i & 1)
      cout << r-- << " ";
    else
      cout << l++ << " ";
  }
  if (k & 1) {
    for (int i = l; i <= r; i++) cout << i << " ";
    cout << '\n';
  } else {
    for (int i = r; i >= l; i--) cout << i << " ";
    cout << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int T;
  T = 1;
  while (T--) {
    Run_Case();
  }
  return 0;
}
