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;
inline int gcd(int x, int y) {
  for (int t; y; t = x % y, x = y, y = t)
    ;
  return x;
}
inline long long gcd(long long x, long long y) {
  for (long long t; y; t = x % y, x = y, y = t)
    ;
  return x;
}
inline void read(int &x) {
  char cc = getchar();
  while (cc < '0' || cc > '9') cc = getchar();
  x = 0;
  while (cc >= '0' && cc <= '9') {
    x = x * 10 + cc - '0';
    cc = getchar();
  }
}
int ri() {
  int x;
  scanf("%d", &x);
  return x;
}
long long rll() {
  long long x;
  scanf("%lld", &x);
  return x;
}
int main() {
  int n, k, p;
  read(n);
  read(k);
  for (int i = (int)(1); i <= (int)(n - k); i++) cout << i << ' ';
  p = n - k + 1;
  for (int i = (int)(1); i <= (int)(k); i++) {
    if (i % 2)
      cout << n-- << ' ';
    else
      cout << p++ << ' ';
  }
  return 0;
}
