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 int maxn = 1e5 + 11;
int n, k;
int num[maxn];
bool used[maxn];
int a[maxn];
int flag;
bool cmp(int a, int b) { return abs(a - flag) < abs(b - flag); }
int main() {
  ios::sync_with_stdio(0);
  while (cin >> n >> k) {
    memset(used, 0, sizeof used);
    int now = 1, cnt = 1;
    while (1) {
      if (now > k) break;
      used[cnt] = 1;
      num[now] = cnt++;
      now += 2;
    }
    now = 2, cnt = n;
    while (1) {
      if (now > k) break;
      used[cnt] = 1;
      num[now] = cnt--;
      now += 2;
    }
    flag = num[k];
    cnt = 0;
    for (int i = 1; i <= n; i++)
      if (!used[i]) a[++cnt] = i;
    sort(a + 1, a + 1 + cnt, cmp);
    for (int i = k + 1; i <= n; i++) {
      num[i] = a[i - k];
    }
    for (int i = 1; i <= n; i++) {
      if (i == n)
        cout << num[i] << endl;
      else
        cout << num[i] << " ";
    }
  }
  return 0;
}
