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.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;

/* abhi2601 */

public class Q2 implements Runnable{

    final static long mod = (long)1e9 + 7;
    ArrayList<Integer>[]a;
    boolean visited[];
    HashMap<String,Integer>hm=new HashMap<>();
    int c=0;
    static long gcd(long x,long y){
        if(y==0) return x;
        else return gcd(y,x%y);
    }
    void DFS(int v,boolean visited[])
    {
        visited[v] = true;
        System.out.print(v+" ");
        Iterator<Integer> i = a[v].listIterator();
        while (i.hasNext())
        {
            int n = i.next();
            if (!visited[n])
                DFS(n,visited);
        }
    }
    void BFS(int v){
        Queue<Integer>q=new LinkedList<>();
        q.add(v);
        Iterator<Integer>i=a[v].iterator();
        while(i.hasNext()){
            int x=i.next();
            String s=v+"-"+x;
            if(!visited[x] && hm.get(s).equals(0)){
                //System.out.println(v+" "+x);
                visited[x]=true;
                c++;
                q.add(x);
                BFS(x);

            }
        }
    }
    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        int n=sc.nextInt();
        int k=sc.nextInt();
        a=new ArrayList[n+1];
        String s;
        for(int i=0;i<=n;i++){
            a[i]=new ArrayList<>();
        }
        for(int i=1;i<n;i++){
            int a1=sc.nextInt();
            int a2=sc.nextInt();
            int x=sc.nextInt();
            a[a1].add(a2);
            a[a2].add(a1);
            s=a1+"-"+a2;
            hm.put(s,x);
            s=a2+"-"+a1;
            hm.put(s,x);
        }
        visited=new boolean[n+1];
        int aa[]=new int[n+1];
        for(int i=1;i<=n;i++){
            if(!visited[i]){
                visited[i]=true;
                c=1;
                BFS(i);
                aa[c]++;
                //w.println(i+" "+c);
            }
        }
        long fre[]=new long[n+1];
        long p;
        for(int i=1;i<=n;i++){
            p=1L;
            for(int j=1;j<=k;j++){
                p=(p*(long)i)%mod;
            }
            fre[i]=p;
        }
        long ans=fre[n];
        for(int i=1;i<=n;i++){
            if(aa[i]>0){
                long temp=((long)aa[i]*fre[i])%mod;
                ans=(ans+mod-temp)%mod;
            }
        }
        w.println(ans);
        w.close();
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int 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 String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        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 double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString()
        {
            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 String next()
        {
            return readString();
        }

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

    public static void main(String args[]) throws Exception
    {
        new Thread(null, new Q2(),"cf3",1<<26).start();
    }
}