Diverse Permutation

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

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Description

Permutationp is an ordered set of integers p₁,   p₂,   ...,   p_n, consisting of n distinct positive integers not larger than n. We'll denote asn the length of permutation p₁,   p₂,   ...,   p_n.

Your task is to find such permutation p of length n, that the group of numbers |p₁ - p₂|, |p₂ - p₃|, ..., |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.

Sample Input

Input

3 2

Output

1 3 2

Input

3 1

Output

1 2 3

Input

5 2

Output

1 3 2 4 5

Hint

By |x| we denote the absolute value of number x.

1 #include 
         
           2 #include 
          
            3 int main() 4 { 5     int n,k; 6     int i,j; 7     int a[100005]; 8     while(scanf("%d %d",&n,&k)!=EOF) 9     {10         memset(a,0,sizeof(a));11         int j=k+2,num=1;12         a[1]=1;13         printf("1");14         while(k)15         {16             if(num-k>0 && a[num-k]==0)17             {18                 printf(" %d",num-k);19                 num=num-k;20                 a[num]=1;21             }22             else23             {24                 printf(" %d",num+k);25                 num=num+k;26                 a[num]=1;27             }28             k--;29         }30         for(i=j;i<=n;i++)31         {32             printf(" %d",i);33         }34         printf("\n");35     }    36     return 0;37 }