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 < 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 ai and bi (1 ≤ ai, bi ≤ 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).

<image>

There are <image> 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.
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class BearandTreeJumps {

	static int n, k;
	static ArrayList<Integer> adj[] = new ArrayList[200_000];
	static long val[][] = new long[200_000][5];
	static long size[][] = new long[200_000][5];
	static long szTmp [][] = new long[200_000][5];
	static long valTmp [][] = new long[200_000][5];
	
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		n = sc.nextInt(); k = sc.nextInt();
		
		for(int i = 0; i < n; ++i) adj[i] = new ArrayList<Integer>();
		int u, v;
		for(int i = 0; i < n - 1; ++i) {
			u = sc.nextInt() - 1; v = sc.nextInt() - 1;
			adj[u].add(v); adj[v].add(u);
		}
		
		dfsDown(0, -1);
		dfsUp(0, -1);
		
		long sum = 0;
		
		for(int i = 0; i < n; ++i) {
			for(int j = 0; j < k; ++j) {
				if(j > 0)
					sum += (val[i][j] + size[i][j] * (k - j)) / k;
				else
					sum += (val[i][j] / k);
			}
		}
		
		out.println(sum / 2);
		
		out.flush();
		out.close();
	}
	
	private static void dfsDown(int i, int parent) {
		size[i][0] = 1;
		val[i][0] = 0;
		
		for(int v : adj[i]) {
			if(v == parent) continue;
			
			dfsDown(v, i);
			
			for(int j = 0; j < k; ++j) {
				val[i][(j + 1) % k] += val[v][j] + size[v][j];
				size[i][(j + 1) % k] += size[v][j]; 
			}
		}
	}
	
	static int fix(int i) {
		return ((i % k) + k) % k;
	}
	
	private static void dfsUp(int i, int p) {
		if(i != 0) {
			for(int j = 0; j < k; ++j) {
				szTmp[i][j] = size[i][j] + size[p][fix(j - 1)] - size[i][fix(j - 2)];
				valTmp[i][j] = val[i][j] + val[p][fix(j - 1)] - (val[i][fix(j - 2)] + size[i][fix(j - 2)]) + size[p][fix(j - 1)] - size[i][fix(j - 2)];
			}
			for(int j = 0; j < k; ++j) {
				size[i][j] = szTmp[i][j];
				val[i][j] = valTmp[i][j];
			}
		}
		
		for(int v : adj[i]) {
			if(v != p)
				dfsUp(v, i);
		}
	}

	static class Scanner{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public Scanner(FileReader r){	br = new BufferedReader(r);}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}

		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}

		public double nextDouble() throws IOException { return Double.parseDouble(next()); }

		public boolean ready() throws IOException {return br.ready();}
	}
}