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;
int on_bit(int x, int pos) {
  x |= (1 << pos);
  return x;
}
int off_bit(int x, int pos) {
  x &= ~(1 << pos);
  return x;
}
bool is_on_bit(int x, int pos) { return ((x & (1 << pos)) != 0); }
int flip_bit(int x, int pos) {
  x ^= (1 << pos);
  return x;
}
int lsb(int x) { return x & (-x); }
int on_bit_all(int x, int pos) {
  x = (1 << pos) - 1;
  return x;
}
const double EPS = 1e-9;
const double PI = 2 * acos(0.0);
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
int add(long long a, long long b) { return ((a % MOD) + (b % MOD)) % MOD; }
int sub(long long a, long long b) { return ((a % MOD) - (b % MOD)) % MOD; }
int mult(long long a, long long b) { return ((a % MOD) * (b % MOD)) % MOD; }
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
int main() {
  vector<int> res;
  int n, k;
  scanf("%d%d", &n, &k);
  int l = 1, r = n;
  int u = 1;
  for (int i = 0; i < (int)k; i++) {
    if (u) {
      res.push_back(l);
      l++;
    } else {
      res.push_back(r);
      r--;
    }
    u ^= 1;
  }
  if (k & 1)
    for (int i = l; i < (int)r + 1; i++) res.push_back(i);
  else
    for (int i = r; i >= (int)l; i--) res.push_back(i);
  for (int i = 0; i < (int)((int)(res).size()); i++) {
    if (i) printf(" ");
    printf("%d", res[i]);
  }
  puts("");
  return 0;
}
