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 long long read() {
  long long x = 0, neg = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') neg = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return x * neg;
}
long long num[1000005];
signed main() {
  long long n = read(), k = read();
  long long neg = -1;
  cout << 1 << ' ';
  long long x = 1;
  num[1] = 1;
  for (long long i = k; i >= 1; --i) {
    neg = -neg;
    cout << x + neg * i << ' ';
    x = x + neg * i;
    num[x] = 1;
  }
  for (long long i = 1; i <= n; ++i) {
    if (!num[i]) {
      cout << i << ' ';
    }
  }
  return 0;
}
