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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class C implements Runnable {

    List<Integer>[] r;
    long[][] down;
    int n, k;
    long sum;
    long[] rem;

    long dfs(int q, int p) {
        long res = 0;
        for (int z : r[q]) {
            if (z != p) {
                res += dfs(z, q);
                for (int i = 0; i < k; i++) down[q][i] += down[z][(i + k - 1) % k];
            }
        }
        res++;
        if (p != -1) sum += res * (n - res);
        long[] tmp = new long[k];
        for (int z : r[q]) {
            if (z != p) {
                for (int i = 0; i < k; i++) down[q][i] -= down[z][(i + k - 1) % k];
                for (int i = 0; i < k; i++) {
                    for (int j = 0; j < k; j++) {
                        tmp[(i + j + 1) % k] += down[q][i] * down[z][j];
                    }
                }
                for (int i = 0; i < k; i++) down[q][i] += down[z][(i + k - 1) % k];
            }
        }
        for (int i = 0; i < k; i++) rem[i] += tmp[i] / 2 + down[q][i];
        down[q][0]++;
        return res;
    }

    void dfs2(int q, int p, int[] a) {
        if (p != -1) {
            for (int i = 0; i < k; i++) {
                for (int j = 0; j < k; j++) {
                    rem[(i + j + 1) % k] += a[i] * down[q][j];
                }
            }
        }
        int[] t = new int[k];
        for (int i = 0; i < k; i++) t[i] = a[(i + k - 1) % k];
        for (int i = 0; i < k; i++) t[i] += down[q][i];
        for (int z : r[q]) {
            if (z != p) {
                for (int i = 0; i < k; i++) t[i] -= down[z][(i + k - 1) % k];
                dfs2(z, q, t);
                for (int i = 0; i < k; i++) t[i] += down[z][(i + k - 1) % k];
            }
        }
    }

    void solve() throws IOException {
        n = nextInt();
        k = nextInt();
        r = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) r[i] = new ArrayList<>();
        for (int i = 0; i < n - 1; i++) {
            int a = nextInt(), b = nextInt();
            r[a].add(b); r[b].add(a);
        }
        down = new long[n + 1][k];
        sum = 0;
        rem = new long[k];
        dfs(1, -1);
//        dfs2(1, -1, new int[k]);
        for (int i = 1; i < k; i++) {
            sum += rem[i] * (k - i);
        }
        out.println(sum / k);
    }

    public static void main(String[] args) {
	    new Thread(null, new C(), "name", 1 << 27).start();
    }

    @Override
    public void run() {
        try {
            solve();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        } finally {
            out.close();
        }
    }

    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);
    StringTokenizer st;

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

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