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 bool dist = true;
const int tests = 3;
void solvea(istream *in) {
  int n, k;
  *in >> n >> k;
  for (int i = 0; i < n - k; i++) {
    cout << (i + 1) << " ";
  }
  bool max = true;
  int maxVal = n;
  int minVal = n - k + 1;
  for (int i = n - k; i < n; i++) {
    cout << (max ? (maxVal) : (minVal)) << " ";
    if (max) {
      maxVal--;
    } else {
      minVal++;
    }
    max = !max;
  }
  cout << endl;
}
int main(int argc, char **argv) {
  istream *in;
  in = &cin;
  if (!dist) {
    in = new ifstream("ina.txt");
  }
  for (int i = 0; i < (dist ? 1 : tests); i++) {
    solvea(in);
  }
  return 0;
}
