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.*;

public class Solu {
    static StringBuffer str = new StringBuffer();
    static InputReader in = new InputReader(System.in);
    static int mm = 1000000007;
    static int n;
    static ArrayList<Integer> tree[];
    static boolean vis[];
    static long cnt=0;
    public static void main(String[] args) {
        int t, i, j, tt, m,k;
        t = 1;
        for (tt = 0; tt < t; tt++) {
            n=in.nextInt();
            tree=new ArrayList[n];
            vis=new boolean[n];
            for(i=0;i<n;i++){
                tree[i]=new ArrayList<>();
            }
            k=in.nextInt();
            for(i=0;i<n-1;i++){
                int x=in.nextInt()-1;
                int y=in.nextInt()-1;
                int col=in.nextInt();
                if(col==0){
                    tree[x].add(y);
                    tree[y].add(x);
                }
            }
            long ans=0;
            for(i=0;i<n;i++){
                if(!vis[i]){
                    cnt=0;
                    dfs(i);
                    ans=(ans+power(cnt,k,mm))%mm;
                }
            }
            long hp=(power(n,k,mm)-ans+mm)%mm;
            ap(hp+"\n");
        }
        pn();
    }
    static void dfs(int x){
        vis[x]=true;
        cnt++;
        for(Integer it:tree[x]){
            if(!vis[it]){
                dfs(it);
            }
        }
    }
    static class hog {

        char ch;
    }
    static final Comparator<Entity> com = new Comparator<Entity>() {
        public int compare(Entity x, Entity y) {
            int xx = Integer.compare(x.a, y.a);
            if (xx == 0) {
                return Long.compare(y.c, x.c);
            } else {
                return xx;
            }
        }
    };

    static class Pair {

        int a, b, c;

        Pair(int x, int y, int z) {
            a = x;
            b = y;
            c = z;
        }
    }

    static class Entity {

        int a;
        int c;

        Entity(int p, int q) {
            a = p;
            c = q;
        }
    }

    static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcdi(int a, int b) {
        return (b == 0) ? a : gcdi(b, a % b);
    }

    static long power(long x, int y, int m) {
        if (y == 0) {
            return 1;
        }
        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;
        return (y % 2 == 0) ? p : (x * p) % m;
    }

    public static void ap(String st) {
        str.append(st);
    }

    public static void pn() {
        System.out.println(str);
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

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

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

        public void skip(int x) {
            while (x-- > 0) {
                read();
            }
        }

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

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

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

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

            return res.toString();
        }

        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }


        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 boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1) {
                read();
            }
            return value != -1;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}
