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;
inline int getnum() {
  char c = getchar();
  int num, sign = 1;
  for (; c < '0' || c > '9'; c = getchar())
    if (c == '-') sign = -1;
  for (num = 0; c >= '0' && c <= '9';) {
    c -= '0';
    num = num * 10 + c;
    c = getchar();
  }
  return num * sign;
}
bool A[100006];
int main() {
  int n = getnum(), k = getnum(), l = 1;
  for (int i = 1; i <= k / 2; i++) {
    printf("%d %d ", i, n - i + 1);
    A[i] = true;
    A[n - i + 1] = true;
    if (i == k / 2 && k % 2) {
      printf("%d ", i + 1);
      A[i + 1] = true;
    }
  }
  if (k % 2) {
    for (int i = 1; i <= n; i++)
      if (!A[i]) printf("%d ", i);
  } else {
    for (int i = n; i >= 1; i--)
      if (!A[i]) printf("%d ", i);
  }
}
