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;
double sqr(double x) { return x * x; }
double distsqr(double x, double y, double a, double b) {
  return sqr((x - a)) + sqr((y - b));
}
double cosine_angle(double a, double b, double c) {
  return (double)(sqr(a) + sqr(b) - sqr(c)) / ((double)2.0 * a * b);
}
int num[100001];
bool taken[100001];
int main() {
  int i = 0, j, n, k;
  scanf("%d %d", &n, &k);
  num[i] = 1;
  taken[num[i++]] = 1;
  while (k--) {
    if (i & 1)
      num[i] = num[i - 1] + k + 1;
    else
      num[i] = num[i - 1] - k - 1;
    taken[num[i]] = 1;
    i++;
  }
  for (j = 0; i < n; j++) {
    if (taken[j + 1])
      ;
    else {
      num[i++] = j + 1;
    }
  }
  for (i = 0; i < n; i++) printf("%d ", num[i]);
  return 0;
}
