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;
bool arr[100000 + 2];
long long n, k;
int main() {
  cin >> n >> k;
  if (k == 2) {
    cout << 1 << " " << 3 << " " << 2 << " ";
    for (int i = 4; i <= n; i++) cout << i << " ";
  } else if (k == 1) {
    for (int i = 1; i <= n; i++) cout << i << " ";
  } else {
    long long num = 1, diff = k;
    for (int i = 1; i <= n; i++) {
      if (i & 1) {
        cout << num << " ";
        arr[num]++;
      } else {
        cout << num + diff << " ";
        arr[num + diff] = 1;
        num++;
        while (arr[num]) num++;
        diff = diff - 2;
        if (diff <= 0) break;
      }
    }
    for (int i = 1; i <= n; i++) {
      if (!arr[i]) cout << i << " ";
    }
  }
  cout << endl;
  return 0;
}
