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 long long MAX = 2e5 + 10;
vector<long long> rpta;
int main() {
  long long n, k;
  cin >> n >> k;
  long long dif = n - 1;
  long long fact = 1;
  rpta.push_back(1);
  long long sobra = n - 1;
  long long ult;
  while (k > 1) {
    ult = rpta.back() + dif * fact;
    rpta.push_back(ult);
    fact *= -1;
    k--;
    dif--;
    sobra--;
  }
  for (long long i = (long long)(0); i < (long long)(sobra); i++)
    rpta.push_back(rpta.back() + fact);
  for (long long i = (long long)(0); i < (long long)(n); i++)
    cout << rpta[i] << " \n"[i == n - 1];
}
