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*.
The first line of the input contains two integers *n* and *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*<sub class="lower-index">*i*</sub> and *b*<sub class="lower-index">*i*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub> ≤ *n*) — the indices on vertices connected with *i*-th edge.

It's guaranteed that the given edges form a tree.
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 <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/c0295201207e28a36e641d8cf599f45986059e71.png" style="max-width: 100.0%;max-height: 100.0%;"/> 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 5·2 + 10·1 = 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 3·1 = 3.
print("_RANDOM_GUESS_1689447896.9626553")# 1689447896.9626758