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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Wolfgang Beyer
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        int n;
        int k;
        Node[] nodes;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            k = in.nextInt();
            nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
            }

            for (int i = 0; i < n - 1; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                nodes[u].neighbors.add(v);
                nodes[v].neighbors.add(u);
            }

            // calculate solution for k = 1
            long result = dfsPairwiseDistanceSum(0, 0);
            //out.println("total pw distance sum: " + result);

            if (k > 1) {
                dfsCalculateAdjustments(0, 0);
                for (int i = 1; i < k; i++) {
                    long pathAnz = nodes[0].startingPaths[i] + nodes[0].containedPaths[i];
                    //out.println("Path Restklasse " + i + ": " + pathAnz);
                    result += ((long) (k - i)) * (nodes[0].startingPaths[i] + nodes[0].containedPaths[i]);
                }
                result /= k;
            }

            out.println(result);
        }

        void dfsCalculateAdjustments(int idx, int parentIdx) {
            for (int child : nodes[idx].neighbors) {
                if (child != parentIdx) {

                    dfsCalculateAdjustments(child, idx);

                    //nodes[idx].containedPaths[1]++;
                    for (int i = 0; i < k; i++) {
                        for (int j = 0; j < k; j++) {
                            nodes[idx].containedPaths[(i + j + 1) % k] += nodes[idx].startingPaths[i] * nodes[child].startingPaths[j];
                        }
                        //nodes[idx].containedPaths[(i + 1) % k] += nodes[child].startingPaths[i];
                        nodes[idx].containedPaths[(i + 1) % k] += nodes[idx].startingPaths[i];
                        nodes[idx].containedPaths[i] += nodes[child].containedPaths[i] + nodes[child].startingPaths[i];
                    }

                    for (int i = 0; i < k; i++) {
                        nodes[idx].startingPaths[(i + 1) % k] += nodes[child].startingPaths[i];
                    }
                    nodes[idx].startingPaths[1]++;

                }
            }
        }

        long dfsPairwiseDistanceSum(int idx, int parentIdx) {
            long result = 0;
            int sizeOfSubtree = 1;
            for (int child : nodes[idx].neighbors) {
                if (child != parentIdx) {
                    result += dfsPairwiseDistanceSum(child, idx);
                    sizeOfSubtree += nodes[child].sizeOfSubtree;
                    result += (long) nodes[child].sizeOfSubtree * (n - nodes[child].sizeOfSubtree);
                }
            }
            nodes[idx].sizeOfSubtree = sizeOfSubtree;
            //System.out.println(idx + ": " + result);
            return result;
        }

        class Node {
            List<Integer> neighbors;
            int sizeOfSubtree;
            long[] startingPaths;
            long[] containedPaths;

            public Node() {
                neighbors = new ArrayList<>();
                sizeOfSubtree = 0;
                containedPaths = new long[k];
                startingPaths = new long[k];
            }

        }

    }

    static class InputReader {
        private static BufferedReader in;
        private static StringTokenizer tok;

        public InputReader(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

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

        public String next() {
            try {
                while (tok == null || !tok.hasMoreTokens()) {
                    tok = new StringTokenizer(in.readLine());
                }
            } catch (IOException ex) {
                System.err.println("An IOException was caught :" + ex.getMessage());
            }
            return tok.nextToken();
        }

    }
}

