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 ll = long long;
const int INF = 0x3f3f3f3f;
using namespace std;
int n, k, ok[100001];
int main() {
  scanf("%d%d", &n, &k);
  int st = 1;
  int r = 0;
  ok[1] = 1;
  printf("1 ");
  while (k > 1) {
    if (r) {
      st -= k;
    } else {
      st += k;
    }
    printf("%d ", st);
    ok[st] = 1;
    r = !r;
    k--;
  }
  for (int i = 1; i <= n; ++i) {
    if (!ok[i]) {
      printf("%d ", i);
    }
  }
  puts("");
  return 0;
}
