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.

//Let us all take a moment and laugh at Real Madrid !! Hahahahahahaha hahahahahahahaha....
import java.util.*;
import java.io.*;
import java.math.*;
public class Main
{
    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;}
        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 long l(){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 int i(){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 double d() throws IOException {return Double.parseDouble(next()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
    }
    static int newGroupNo;
    public static void main(String[] args)throws IOException {
        /*
inputCopy
4 4
1 2 1
2 3 1
3 4 1
outputCopy
252
inputCopy
4 6
1 2 0
1 3 0
1 4 0
outputCopy
0
inputCopy
3 5
1 2 1
2 3 0
outputCopy
210

4 3
1 3 0
1 4 0
1 2 1
        */
        PrintWriter pw = new PrintWriter(System.out);
        FastReader fr = new FastReader();
        int n=fr.i();
        int k=fr.i();
        BigInteger ans=new BigInteger(n+"");
        long mod=1_000_000_007;
        BigInteger bigMod=new BigInteger(mod+"");
        ans=ans.pow(k);
        Node [] nodeArr=new Node[n+1];
        for(int ni=1;ni<=n;++ni)
        {
            nodeArr[ni]=new Node(ni);
        }
        LinkedList<Edge> adjList []=new LinkedList[n+1];
        for(int ni=1;ni<=n;++ni)
        {
            adjList[ni]=new LinkedList<>();
        }
        for(int ni=1;ni<=n-1;++ni)
        {
            int source=fr.i();
            int dest=fr.i();
            int type=fr.i();
            if(type==1)
            {
                nodeArr[source].incomingBlack=true;
                nodeArr[dest].incomingBlack=true;
            }
            Edge e1=new Edge(source,dest,type);
            Edge e2=new Edge(dest,source,type);
            adjList[source].add(e1);
            adjList[dest].add(e2);
        }
        boolean [] visited=new boolean[n+1];
        newGroupNo=2;
        DFS(adjList,nodeArr,visited,1,1);
        int [] groupCount=new int[n+2];
        for(int ni=1;ni<=n;++ni)
        {
            ++groupCount[nodeArr[ni].group];
        }
       System.err.println(Arrays.toString(groupCount));
        for(int i=1;i<=n+1;++i)
        {
            System.err.println(ans);
            ans=ans.subtract(new BigInteger(groupCount[i]+"").pow(k));
        }
        ans=ans.mod(bigMod);
        pw.println(ans);
        pw.flush();
        pw.close();
    }
    public static void DFS(LinkedList<Edge> [] adjList,Node [] nodeArr,boolean [] visited,int source,int group)
    {
        if(visited[source])
            return;
        visited[source]=true;

        if(nodeArr[source].incomingBlack)
        {
            group=newGroupNo;
            ++newGroupNo;
        }
        nodeArr[source].group=group;
        Iterator<Edge> itr=adjList[source].listIterator();
        while(itr.hasNext())
        {
            Edge e=itr.next();
            if(!visited[e.dest])
            {
                DFS(adjList,nodeArr,visited,e.dest,group);
            }
        }
    }
    static class Node
    {
        Node left;
        Node right;
        int id;
        int group;
        boolean incomingBlack;
        Node(int i)
        {
            id=i;
            group=0;
            incomingBlack=false;
            left=null;
            right=null;
        }
    }
    static class Edge
    {
        int source;
        int dest;
        int type;
        Edge(int s,int d,int t)
        {
            source=s;
            dest=d;
            type=t;
        }
    }
}
