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;
int n, k;
int a[100000 + 10];
int main() {
  while (cin >> n >> k) {
    int len = k / 2;
    int l = 1, r = n;
    int i = 1;
    for (int j = (1); j <= (len); ++j) {
      a[i++] = l++;
      a[i++] = r--;
    }
    for (int j = (i); j <= (n); ++j) a[j] = l++;
    if (k % 2 == 0 && k != n - 1) swap(a[1], a[2]);
    for (int i = (1); i <= (n); ++i) printf("%d ", a[i]);
    printf("\n");
  }
}
