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;
int main() {
  long long m, n, i, j, k, l;
  while (cin >> n >> k) {
    l = n, j = 1;
    vector<long long> v, v1;
    for (long long i = 1; i <= n; i++) {
      if (i % 2 == 1 && i == 1) {
        v.push_back(j);
        j++;
      }
      if (i % 2 == 1 && i != 1) {
        v.push_back(j);
        j++;
      }
      if (i % 2 == 0) {
        v.push_back(l);
        l--;
      }
    }
    for (long long i = 0; i < k; i++) v1.push_back(v[i]);
    if (k % 2 == 0)
      sort(v.begin() + (k), v.end(), greater<int>());
    else
      sort(v.begin() + (k), v.end());
    for (i = k; i < v.size(); i++) v1.push_back(v[i]);
    for (long long i = 0; i < v1.size(); i++) cout << v1[i] << " ";
    printf("\n");
    v.clear(), v1.clear();
  }
}
