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>
#pragma GCC optimize("-O3")
using namespace std;
long long int MOD = 998244353;
long long int NUM = 1e9 + 7;
long long int MPOW(long long int a, long long int b, long long int m) {
  if (b == 0) return 1;
  long long int x = MPOW(a, b / 2, m);
  x = (x * x) % m;
  if (b % 2 == 1) x = (x * a) % m;
  return x;
}
long long int MINV(long long int a, long long int m) {
  return MPOW(a, m - 2, m);
}
long long int MFACT(long long int n, long long int m) {
  if (m <= n)
    return 0;
  else if (n == 0)
    return 1;
  else
    return ((MFACT(n - 1, m) * n) % m);
}
inline long long int max(long long int a, long long int b) {
  return (a > b) ? a : b;
}
inline long long int min(long long int a, long long int b) {
  return (a < b) ? a : b;
}
inline void swap(long long int &a, long long int &b) {
  long long int temp = a;
  a = b;
  b = temp;
  return;
}
inline long long int max3(long long int a, long long int b, long long int c) {
  return max(a, max(b, c));
}
inline long long int min3(long long int a, long long int b, long long int c) {
  return min(a, min(b, c));
}
int main() {
  long long int n, k;
  cin >> n >> k;
  long long int j, it;
  j = 1, it = k + 1;
  for (long long int i = 1; i <= k + 1; i++) {
    if (i % 2) {
      cout << j << ' ';
      j++;
    } else {
      cout << it << ' ';
      it--;
    }
  }
  for (long long int i = k + 2; i <= n; i++, j) {
    cout << i << ' ';
  }
  return 0;
}
