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;
long long l, r;
int a[100001];
void init() {
  cin >> l >> r;
  int b = 1;
  int tot = r;
  a[1] = 1;
  for (int i = 2; i <= r + 1; i++) {
    if (b == 1) {
      a[i] = a[i - 1] + tot;
      b = 0;
      tot--;
    } else {
      a[i] = a[i - 1] - tot;
      b = 1;
      tot--;
    }
  }
  for (int i = r + 2; i <= l; i++) a[i] = i;
  for (int i = 1; i <= l; i++) cout << a[i] << " ";
  cout << endl;
}
int main() {
  init();
  return 0;
}
