Limak is a little polar bear. He lives in a tree that consists of $n$ vertices, numbered $1$ through $n$.
Limak recently learned how to jump. He can jump from a vertex to any vertex within distance at most $k$.
For a pair of vertices $(s,t)$ we define $f(s,t)$ as the minimum number of jumps Limak needs to get from $s$ to $t$.
Your task is to find the sum of $f(s,t)$ over all pairs of vertices $(s,t)$ such that $s<t$.

The first line of the input contains two integers $n,k\ (2≤n≤200,000,\ 1≤k≤5)$ − the number of vertices in the tree and the maximum allowed jump distance respectively.

The next $n-1$ lines describe edges in the tree. The $i$-th of those lines contains two integers $a_i,b_i\ (1≤a_i,b_i≤n)$ − the indices on vertices connected with $i$-th edge.

It's guaranteed that the given edges form a tree.

Print one integer, denoting the sum of $f(s,t)$ over all pairs of vertices $(s,t)$ such that $s<t$.

20

the given tree has $6$ vertices and it's displayed on the drawing below. Limak can jump to any vertex within distance at most $2$. 

For example, from the vertex $5$ he can jump to any of vertices: 1,2 and 4 (well, he can also jump to the vertex 5 itself).

There are $\frac{n(n-1)}{2}=15$ pairs of vertices $(s,t)$ such that $s<t$. 

For $5$ of those pairs Limak would need two jumps: (1,6),(3,4),(3,5),(3,6),(5,6). For other $10$ pairs one jump is enough. So, the answer is 5·2+10·1=20.

3

Limak can jump between every two vertices directly. There are 3 pairs of vertices (s<t), so the answer is 3·1=3.