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;
void print(int* x, int n) {
  for (int i = 0; i < n; i++) {
    if (i != 0) cout << " ";
    cout << x[i];
  }
  cout << endl;
}
int main() {
  int n, k;
  cin >> n >> k;
  if (k == 1) {
    for (int i = 0; i < n; i++) cout << i + 1 << " ";
    cout << endl;
    return 0;
  }
  int x[100001];
  x[0] = k + 1;
  int m = k;
  set<int> ss;
  for (int i = 1; i <= k; i++) {
    x[i] = x[i - 1] - m;
    if (x[i] < 1 || ss.find(x[i]) != ss.end()) {
      x[i] = x[i - 1] + m;
      while (ss.find(x[i]) != ss.end()) {
        x[i]++;
      }
    }
    ss.insert(x[i]);
    m--;
  }
  for (int i = k + 1; i < n; i++) {
    x[i] = i + 1;
  }
  print(x, n);
  return 0;
}
