You are given a tree (a connected undirected graph without cycles) of n vertices. Each of the n - 1 edges of the tree is colored in either black or red.

You are also given an integer k. Consider sequences of k vertices. Let's call a sequence [a_1, a_2, …, a_k] good if it satisfies the following criterion:

  * We will walk a path (possibly visiting same edge/vertex multiple times) on the tree, starting from a_1 and ending at a_k. 
  * Start at a_1, then go to a_2 using the shortest path between a_1 and a_2, then go to a_3 in a similar way, and so on, until you travel the shortest path between a_{k-1} and a_k.
  * If you walked over at least one black edge during this process, then the sequence is good. 

<image>

Consider the tree on the picture. If k=3 then the following sequences are good: [1, 4, 7], [5, 5, 3] and [2, 3, 7]. The following sequences are not good: [1, 4, 6], [5, 5, 5], [3, 7, 3].

There are n^k sequences of vertices, count how many of them are good. Since this number can be quite large, print it modulo 10^9+7.

Input

The first line contains two integers n and k (2 ≤ n ≤ 10^5, 2 ≤ k ≤ 100), the size of the tree and the length of the vertex sequence.

Each of the next n - 1 lines contains three integers u_i, v_i and x_i (1 ≤ u_i, v_i ≤ n, x_i ∈ \{0, 1\}), where u_i and v_i denote the endpoints of the corresponding edge and x_i is the color of this edge (0 denotes red edge and 1 denotes black edge).

Output

Print the number of good sequences modulo 10^9 + 7.

Examples

Input


4 4
1 2 1
2 3 1
3 4 1


Output


252

Input


4 6
1 2 0
1 3 0
1 4 0


Output


0

Input


3 5
1 2 1
2 3 0


Output


210

Note

In the first example, all sequences (4^4) of length 4 except the following are good: 

  * [1, 1, 1, 1]
  * [2, 2, 2, 2]
  * [3, 3, 3, 3]
  * [4, 4, 4, 4] 



In the second example, all edges are red, hence there aren't any good sequences.

import java.io.*;
import java.util.ArrayList;
import java.util.InputMismatchException;

/**
 * @author solarbeam
 */

public class CF1139C {
    public static void main(String[] args) throws FileNotFoundException, InterruptedException {
        InputStream stream = System.in;
        Logger logger = new Logger();
        if (args.length > 0 && args[0].equals("LOCAL")) {
            File inputFile = new File("resources/input.in");
            stream = new DataInputStream(new FileInputStream(inputFile));
            logger.enableLogging(true, "resources/logs.txt");
        }
        InputReader in = new InputReader(stream);
        PrintWriter out = new PrintWriter(System.out);
        Runnable solver = () -> {
            new Task1().solve(in, out, logger);
        };
        Thread th = new Thread(null, solver, "Task1", 1 << 24);
        th.start();
        th.join();
        out.close();
        logger.close();
    }

    static class Task1 {
        static final int MOD = 1000000007;
        boolean[] marked;
        ArrayList<Integer>[] adj;

        public void solve(InputReader in, PrintWriter out, Logger logger) {
            int n = in.nextInt(), k = in.nextInt();
            adj = new ArrayList[n+1];
            for(int i=1; i<=n; i++)
                adj[i] = new ArrayList<Integer>();

            for(int i=1; i<=n-1; i++){
                int u = in.nextInt(), v = in.nextInt(), type = in.nextInt();
                if(type==0){
                    adj[u].add(v);
                    adj[v].add(u);
                }
            }

            ArrayList<Integer> connectedComponentsSize = new ArrayList<Integer>();
            marked = new boolean[n+1];
            for(int i=1; i<=n; i++){
                if(!marked[i]){
                    int dfsSize = dfs(i);
                    if(dfsSize>1) connectedComponentsSize.add(dfsSize);
                }
            }

            for(int i: connectedComponentsSize){
                logger.log(i+" ");
            }
            logger.logln("");

            long ans = fastPower(n, k) - n;
            for(int i:connectedComponentsSize){
                ans -= fastPower(i, k);
                ans += i;
            }
            out.println(ans);
        }

        int dfs(int v){
            marked[v] = true;
            int ans = 0;
            for(int w:adj[v]){
                if(!marked[w])
                    ans += dfs(w);
            }
            return 1+ans;
        }

        long fastPower(long a, long b){
            long result = 1;
            while(b>0){
                if(b%2==1) result = (result*a)%MOD;
                a = (a*a)%MOD;
                b >>= 1;
            }
            return result%MOD;
        }
    }

    static class Logger {
        private PrintWriter logger;
        private boolean enableLogging;

        public void enableLogging(boolean enableLogging, String filename) {
            this.enableLogging = enableLogging;
            try {
                if (enableLogging) this.logger = new PrintWriter(filename);
            } catch (FileNotFoundException e) {
            }
        }

        public void log(Object s) {
            if (enableLogging) {
                logger.print(s.toString());
            }
        }

        public void logln(Object s) {
            if (enableLogging) {
                logger.println(s.toString());
            }
        }

        public void close() {
            if (enableLogging) logger.close();
        }
    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}
