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 javax.print.attribute.IntegerSyntax;
import java.sql.Array;
import java.util.*;
import java.io.*;
import static java.lang.Math.*;
public class MainS {
    static final long MOD1 = 1_000_000_007, INF = 1_000_000_000_000_000_000L, BASE1 = 47, MOD2 = 1_000_000_007, BASE2 = 31;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;
    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }
    static class O implements Runnable {
        public void run() {
            try {
                magic();
            }
            catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }
    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    static int baap[], weight[];
    static long res;
    static void magic() throws IOException {
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        int n = reader.nextInt(),k = reader.nextInt();
        init(n);
        for(int i=1;i<n;++i) {
            int u = reader.nextInt(), v = reader.nextInt(), type = reader.nextInt();
            if(type==0) {
                un(u, v);
            }
        }
        long ans = 0;
        for(int i=1;i<=n;++i) {
            if(gr(i)==i) {
                ans+=modpow(weight[i],k, MOD1);
                ans%=MOD1;
            }
        }
        writer.println((modpow(n, k, MOD1) - ans + MOD1)%MOD1);
    }
    static void init(int n)
    {
        baap = new int[n+1];
        weight = new int[n+1];
        for(int i=0;i<=n;++i)
        {
            baap[i] = i;
            ++weight[i];
        }
    }
    static int gr(int a)
    {
        if(baap[a]==a)
            return a;
        return baap[a] = gr(baap[a]);
    }
    static boolean un(int a,int b)
    {
        int ra = gr(a);
        int rb = gr(b);
        if(ra==rb)
            return false;
        if(weight[rb]>weight[ra])
        {
            weight[rb]+=weight[ra];
            baap[ra] = rb;
        }
        else
        {
            weight[ra]+=weight[rb];
            baap[rb] = ra;
        }
        return true;
    }
    static long modpow(long x,long y,long mod)
    {
        res = 1;
        while(y>0)
        {
            if((y&1)==1)
                res = (res*x)%mod;
            y>>=1;
            x = (x*x)%mod;
        }
        return res;
    }
}