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>
struct doint {
  int x;
  int y;
};
using namespace std;
int main() {
  int n;
  int k;
  cin >> n >> k;
  doint arr[n];
  arr[0].x = 1;
  arr[0].y = 1;
  for (int i = 1; i < n; i++) {
    arr[i].y = -1;
  }
  for (int i = k - 1; i > 0; i--) {
    arr[k - i].x = arr[k - i - 1].x + (pow(-1, k - i - 1) * (i + 1));
    arr[(arr[k - i].x) - 1].y = 1;
  }
  int mark = 0;
  for (int i = 1; i < n; i++) {
    if (arr[i].y == -1) {
      arr[k + mark].x = i + 1;
      arr[i].y = 1;
      mark++;
    }
  }
  for (int i = 0; i < n; i++) {
    cout << arr[i].x << " ";
  }
}
