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 = 100010;
int a[maxn];
int N, K;
int main() {
  while (scanf("%d%d", &N, &K) != EOF) {
    memset(a, 0, sizeof(a));
    for (int i = 1; i <= N; i += 2) a[i] = (i + 1) / 2;
    int cnt = N;
    for (int i = 2; i <= N; i += 2) a[i] = cnt--;
    if (K & 1)
      sort(a + K + 1, a + N + 1);
    else
      sort(a + K + 1, a + N + 1, greater<int>());
    for (int i = 1; i <= N; i++) printf("%d ", a[i]);
    printf("\n");
  }
  return 0;
}
