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;
template <class T>
T abs(T x) {
  return x > 0 ? x : -x;
}
const long double pi = acos(-1.0);
int n;
int m;
int main() {
  int k;
  scanf("%d %d", &n, &k);
  k--;
  int x = 2, y = n;
  bool f = false;
  printf("1 ");
  while (k > 0) {
    if (f) {
      printf("%d ", x);
      f = false;
      x++;
    } else {
      printf("%d ", y);
      f = true;
      y--;
    }
    k--;
  }
  if (f) {
    for (int i = y; i >= x; i--) {
      printf("%d ", i);
    }
  } else {
    for (int i = x; i <= y; i++) {
      printf("%d ", i);
    }
  }
  return 0;
}
