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;
const int INF = 1 << 30;
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  if (k == 1) {
    printf("1");
    for (int i = 2; i <= n; ++i) printf(" %d", i);
    puts("");
  } else {
    int p1 = 2, p2 = n;
    printf("%d", 1);
    k--;
    int f = 2;
    while (k > 1) {
      if (f == 1) {
        printf(" %d", p1);
        ++p1;
      } else {
        printf(" %d", p2);
        --p2;
      }
      --k;
      f = 3 - f;
    }
    if (f == 2) {
      for (int i = p2; i >= p1; --i) printf(" %d", i);
    } else {
      for (int i = p1; i <= p2; ++i) printf(" %d", i);
    }
    puts("");
  }
  return 0;
}
