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.BufferedInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.Map.Entry;

public class C {
	static int MOD = 1000000007;
	public static void main(String[] args) throws Exception {
		InputReader scan = new InputReader(new BufferedInputStream(System.in));
		int n = scan.nextInt(), k = scan.nextInt();
		UF uf = new UF(n);
		for (int i=0;i<n-1;i++) {
			int s = scan.nextInt() - 1, v = scan.nextInt() - 1, color = scan.nextInt();
			if (color == 0) 
				uf.union(s, v);
		}
		//uf.print();
		Map<Integer, Integer> counts = uf.getCounts();
		//System.out.println(counts);
		long ans=0L;
		for (Entry<Integer, Integer> key: counts.entrySet()) {
			ans = Math.floorMod(ans+pow(key.getValue(), k), MOD);
		}
		ans = Math.floorMod((pow(n, k) - ans),MOD);
		if (ans<0)ans+=MOD;
		System.out.println(ans);
		scan.close();
	}
	
	private static long pow(int n, int k) {
		if (k==1)return (long)n;
		if (k==0)return 1l;
		return Math.floorMod(((long)n*(long)pow(n,k-1)),MOD);
	}

	static class UF {

		private int[] parent;  // parent[i] = parent of i
		private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
		private int count;     // number of components

		public UF(int n) {
			if (n < 0) throw new IllegalArgumentException();
			count = n;
			parent = new int[n];
			rank = new byte[n];
			for (int i = 0; i < n; i++) {
				parent[i] = i;
				rank[i] = 0;
			}
		}

		public Map<Integer, Integer> getCounts() {
			Map<Integer, Integer> map = new HashMap<>();
			for (int i:parent) 
				map.put(i, 1+map.getOrDefault(i, 0));
			return map;
		}

		public void print() {
			System.out.println(Arrays.toString(parent));
		}

		public int find(int p) {
			while (p != parent[p]) {
				parent[p] = parent[parent[p]];    // path compression by halving
				p = parent[p];
			}
			return p;
		}

		public int count() {
			return count;
		}

		public boolean connected(int p, int q) {
			return find(p) == find(q);
		}

		public void union(int p, int q) {
			int rootP = find(p);
			int rootQ = find(q);
			if (rootP == rootQ) return;
			// make root of smaller rank point to root of larger rank
			if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
			else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
			else {
				parent[rootQ] = rootP;
				
				rank[rootP]++;
			}
			count--;
		}
	}

	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 void close() throws IOException {
			this.stream.close();
		}

		public static boolean isWhitespace(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		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 boolean isSpaceChar(int c) {
			if (filter != null) {
				return filter.isSpaceChar(c);
			}
			return isWhitespace(c);
		}

		public interface SpaceCharFilter {

			public boolean isSpaceChar(int ch);
		}

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

		public String nextString() {
			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 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() {
			return Long.parseLong(nextString());
		}

		public Double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public char nextCharacter() {
			return nextString().charAt(0);
		}

		public int[] nextIntArray(int N) {
			int A[] = new int[N];
			for (int i = 0; i < N; i++) {
				A[i] = nextInt();
			}
			return A;
		}

		public long[] nextLongArray(int N) {
			long A[] = new long[N];
			for (int i = 0; i < N; i++) {
				A[i] = nextLong();
			}
			return A;
		}

		public double[] nextDoubleArray(int N) {
			double A[] = new double[N];
			for (int i = 0; i < N; i++) {
				A[i] = nextDouble();
			}
			return A;
		}
	}

	int min(int... a) {
		int min = Integer.MAX_VALUE;
		for (int v : a) {
			min = Math.min(min, v);
		}
		return min;
	}

	long min(long... a) {
		long min = Long.MAX_VALUE;
		for (long v : a) {
			min = Math.min(min, v);
		}
		return min;
	}

	double min(double... a) {
		double min = Double.MAX_VALUE;
		for (double v : a) {
			min = Math.min(min, v);
		}
		return min;
	}

	int max(int... a) {
		int max = Integer.MIN_VALUE;
		for (int v : a) {
			max = Math.max(max, v);
		}
		return max;
	}

	long max(long... a) {
		long max = Long.MIN_VALUE;
		for (long v : a) {
			max = Math.max(max, v);
		}
		return max;
	}

	double max(double... a) {
		double max = Double.MIN_VALUE;
		for (double v : a) {
			max = Math.max(max, v);
		}
		return max;
	}
}