A tree is an undirected connected graph without cycles. The distance between two vertices is the number of edges in a simple path between them.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 \lt t.

Input The first line of the input contains two integers n and k (2 \le n \le 200000, 1 \le k \le 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 ai and bi (1 \le ai,bi \le n)- the indices on vertices connected with i-th edge.It's guaranteed that the given edges form a tree.

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

In the first sample, 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 pairs of vertices (s,t) such that s \lt 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 \cdot 2+10 \cdot 1=20.In the third sample, Limak can jump between every two vertices directly. There are 3 pairs of vertices (s \lt t), so the answer is 3 \cdot 1=3.