Diverse Permutation

Permutation p is an ordered set of integers p ₁,   p ₂,   …,   p _n, consisting of n distinct positive integers not larger than n. We’ll denote as n the length of permutation p ₁,   p ₂,   …,   p _n.

Your task is to find such permutation p of length n, that the group of numbers |p ₁ - p ₂|, |p ₂ - p ₃|, …, |p _n - 1 - p _n| 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.

Solution:

#include <cstring>
#include <vector>
#include  <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <memory.h>
#include <cassert>

using namespace std;

int a[1234567];

int main() {
int n, k;
scanf("%d %d", &n, &k);
a[0] = 1;
int low = 1, high = 1;
for (int i = 1; i <= k; i++) {
    if (i % 2 == 1) {
      a[i] = ++high;
    } else {
      a[i] = --low;
    }
  }
  for (int i = k + 1; i < n; i++) {
    if (a[k] == low) {
      a[i] = a[i - 1] - 1;
    } else {
      a[i] = a[i - 1] + 1;
    }
  }
  int smallest = a[0];
  for (int i = 1; i < n; i++) {
    if (a[i] < smallest) {
      smallest = a[i];
    }
  }
  for (int i = 0; i < n; i++) {
    if (i > 0) printf(" ");
printf("%d", a[i] - smallest + 1);
}
printf("\n");
return 0;
}