No tag edit access

C. Bear and Tree Jumps

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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* < *t*.

Input

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* _{ i} and *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.

Output

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

Examples

Input

6 2

1 2

1 3

2 4

2 5

4 6

Output

20

Input

13 3

1 2

3 2

4 2

5 2

3 6

10 6

6 7

6 13

5 8

5 9

9 11

11 12

Output

114

Input

3 5

2 1

3 1

Output

3

Note

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* < *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* < *t*), so the answer is 3·1 = 3.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/09/2020 09:25:00 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|