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;
#pragma comment(linker, "/STACK:17000000")
const double eps = 1e-9;
const double inf = 1e+9;
int n, k;
int a[100009];
int main() {
  scanf("%d%d", &n, &k);
  int t = n;
  for (int i = 0; i < n; i += 2) {
    a[i] = t--;
  }
  t = 1;
  for (int i = 0; i < n; i++) {
    if (!a[i]) a[i] = t++;
  }
  sort(a + k - 1, a + n);
  if (k & 1) {
    reverse(a + k - 1, a + n);
  }
  for (int i = 0; i < n; i++) {
    printf("%d ", a[i]);
  }
}
