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;
long long gcd(long long a, long long b) {
  if ((a == 0) || (b == 0)) return a + b;
  return gcd(b, a % b);
}
long long pow_mod(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a) % 1000000007;
    a = (a * a) % 1000000007;
    b >>= 1;
  }
  return res;
}
long long arr[1000010];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long T, i, j, N, K, temp1, temp2;
  string st;
  cin >> N >> K;
  temp1 = 1;
  temp2 = K + 1;
  for (i = 1; i <= K + 1; i++) {
    if (i % 2) {
      arr[i] = temp1;
      temp1++;
    } else {
      arr[i] = temp2;
      temp2--;
    }
  }
  for (i = K + 2; i <= N; i++) {
    arr[i] = i;
  }
  for (i = 1; i <= N; i++) {
    cout << arr[i] << " ";
  }
  return 0;
}
