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;
template <class T>
T gcd(T a, T b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
template <class T>
T lcm(T a, T b) {
  return a * b / gcd(a, b);
}
template <class T>
T absolute(T a) {
  if (a > 0)
    return a;
  else
    return -a;
}
inline long long power(long long base, long long p) {
  long long ans = 1;
  while (p > 0) ans *= base, p -= 1;
  return ans;
}
int main() {
  int k, n;
  cin >> n >> k;
  int a = 1, b = n;
  cout << a << ' ';
  a++;
  for (int i = 1; i < k; i++) {
    if (i % 2)
      cout << b-- << ' ';
    else
      cout << a++ << ' ';
  }
  if (k % 2) {
    for (int i = a; i <= b; i++) cout << i << ' ';
  } else
    for (int i = b; i >= a; i--) cout << i << ' ';
  cout << endl;
  return 0;
}
