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 N = 1e5 + 5;
int n, k, ans[N];
int read() {
  int x = 0, y = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') y = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) + ch - '0';
    ch = getchar();
  }
  return x * y;
}
void print(int x) {
  if (x < 0) {
    x = ~(x - 1);
    putchar('-');
  }
  if (x >= 10) print(x / 10);
  putchar(x % 10 + '0');
}
int main() {
  n = read();
  k = read();
  for (int i = k + 1; i <= n; i++) ans[i] = i;
  bool cnt = 1;
  for (int i = k; i >= 1; i--) {
    if (cnt)
      ans[i] = ans[i + 1] - i;
    else
      ans[i] = ans[i + 1] + i;
    cnt ^= 1;
  }
  for (int i = 1; i <= n; i++) print(ans[i]), putchar(' ');
}
