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.util.*;
import java.io.*;

public class C {

	List<Integer>[] tree;
	long[][] cnt, sum;
	long result = 0;
	int k;

	long[] tmpCnt, tmpSum;

	void dfs(int u, int p) {
		cnt[u][0] = 1;
		sum[u][0] = 0;
		for (int t = 0; t < tree[u].size(); t++) {
			int v = tree[u].get(t);
			if (v == p) {
				continue;
			}
			
			dfs(v, u);
			for (int i = 0; i < k; i++) {
				for (int j = 0; j < k; j++) {
					long jumps1 = (sum[u][i] - cnt[u][i] * i) / k;
					long jumps2 = (sum[v][j] - cnt[v][j] * j) / k;
					
					result += jumps1 * cnt[v][j] + jumps2 * cnt[u][i];
					result += (i + j + k - 1) / k * cnt[v][j] * cnt[u][i];
				}
			}
			for (int i = 0; i < k; i++) {
				sum[u][i] += sum[v][i];
				cnt[u][i] += cnt[v][i];
			}
		}
		
		for (int i = 0; i < k; i++) {
			tmpCnt[i] = cnt[u][(i + k - 1) % k];
			tmpSum[i] = sum[u][(i + k - 1) % k] + tmpCnt[i];
		}
		for (int i = 0; i < k; i++) {
			cnt[u][i] = tmpCnt[i];
			sum[u][i] = tmpSum[i];
		}
		
	}

	void solve() {
		int n = in.nextInt();
		k = in.nextInt();
		tree = new List[n];
		for (int i = 0; i < n; i++) {
			tree[i] = new ArrayList<Integer>();
		}
		for (int i = 0; i < n - 1; i++) {
			int from = in.nextInt() - 1, to = in.nextInt() - 1;
			tree[from].add(to);
			tree[to].add(from);
		}
		cnt = new long[n][k];
		sum = new long[n][k];
		tmpCnt = new long[k];
		tmpSum = new long[k];
		
		dfs(0, -1);
		out.println(result);
	}

	FastScanner in;
	PrintWriter out;

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

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

		public int nextInt() {
			return Integer.parseInt(nextToken());
		}

		public long nextLong() {
			return Long.parseLong(nextToken());
		}

		public double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

	public static void main(String[] args) {
		new C().run();
	}
}
