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;
int Set(int N, int pos) { return N = N | (1 << pos); }
int reset(int N, int pos) { return N = N & ~(1 << pos); }
bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
void CI(int &_x) { scanf("%d", &_x); }
void CO(int &_x) { cout << _x; }
template <typename T>
void getarray(T a[], int n) {
  for (int i = 0; i < n; i++) cin >> a[i];
}
template <typename T>
void printarray(T a[], int n) {
  for (int i = 0; i < n - 1; i++) cout << a[i] << " ";
  cout << a[n - 1] << endl;
}
const double EPS = 1e-9;
const int INF = 0x7f7f7f7f;
int dr8[8] = {1, -1, 0, 0, 1, -1, -1, 1};
int dc8[8] = {0, 0, -1, 1, 1, 1, -1, -1};
int dr4[4] = {0, 0, 1, -1};
int dc4[4] = {-1, 1, 0, 0};
int kn8r[8] = {1, 2, 2, 1, -1, -2, -2, -1};
int kn8c[8] = {2, 1, -1, -2, -2, -1, 1, 2};
int main() {
  int n, k;
  cin >> n >> k;
  int pairr = n - 1;
  int distinct_pair = k, non_distinct = pairr - k;
  for (int i = 1; i <= non_distinct + 1; i++) {
    cout << i << " ";
  }
  for (int i = 1, j = n, k = non_distinct + 2; i <= (n - non_distinct - 1);
       i++) {
    if (i % 2 == 1) {
      cout << j << " ";
      j--;
    } else {
      cout << k << " ";
      k++;
    }
  }
}
