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.ArrayList;
    import java.util.StringTokenizer;
    
    public class Solution {
        static final int INF = (int) 1e9;
        static final int mod = (int) (1e9 + 7);
        static final short UNCALC = -1;
        static final int RED = 0, BLACK = 1;
        static ArrayList<Integer> adjList[];
        static int cnt;
        static boolean[] vis;
    
        public static void main(String[] args) throws IOException {
            Scanner sc = new Scanner(System.in);
            PrintWriter out = new PrintWriter(System.out);
            int n = sc.nextInt();
            int k = sc.nextInt();
            adjList = new ArrayList[n];
            for (int i = 0; i < n; i++)
                adjList[i] = new ArrayList<>();
            for (int i = 0; i < n - 1; i++) {
                int u = sc.nextInt() - 1;
                int v = sc.nextInt() - 1;
                int c = sc.nextInt();
                if (c == BLACK) continue;
                adjList[u].add(v);
                adjList[v].add(u);
    
            }
            cnt = 0;
            vis = new boolean[n];
            int ans = 0;
            for (int i = 0; i < n; i++) {
                if (vis[i]) continue;
                cnt = 0;
                dfs(i, i);
                ans = (ans + modPow(cnt, k)) % mod;
            }
            ans = modPow(n, k) - ans;
            while (ans < 0)
                ans += mod;
            out.println(ans % mod);
            out.flush();
            out.close();
        }
    
        static void dfs(int u, int p) {
            vis[u] = true;
            cnt++;
            for (int v : adjList[u])
                if (v != p) dfs(v, u);
        }
    
        static int modPow(int b, int e) {
            long res = 1;
            b %= mod;
            while (e > 0) {
                if ((e & 1) == 1)
                    res = (res * b) % mod;
                b = (int) ((1l * b * b) % mod);
                e >>= 1;
            }
            return (int) res;
        }
    
        static class Scanner {
            StringTokenizer st;
            BufferedReader br;
    
            public Scanner(InputStream system) {
                br = new BufferedReader(new InputStreamReader(system));
            }
    
            public Scanner(String file) throws Exception {
                br = new BufferedReader(new FileReader(file));
            }
    
            public String next() throws IOException {
                while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
                return st.nextToken();
            }
    
            public String nextLine() throws IOException {
                return br.readLine();
            }
    
            public int nextInt() throws IOException {
                return Integer.parseInt(next());
            }
    
            public double nextDouble() throws IOException {
                return Double.parseDouble(next());
            }
    
            public char nextChar() throws IOException {
                return next().charAt(0);
            }
    
            public Long nextLong() throws IOException {
                return Long.parseLong(next());
            }
    
            public boolean ready() throws IOException {
                return br.ready();
            }
    
            public void waitForInput() throws InterruptedException {
                Thread.sleep(3000);
            }
    
            public int[] nextIntArray(int n) throws IOException {
                int[] a = new int[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextInt();
                return a;
            }
    
            public Integer[] nextIntegerArray(int n) throws IOException {
                Integer[] a = new Integer[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextInt();
                return a;
            }
    
            public double[] nextDoubleArray(int n) throws IOException {
                double[] ans = new double[n];
                for (int i = 0; i < n; i++)
                    ans[i] = nextDouble();
                return ans;
            }
    
            public short nextShort() throws IOException {
                return Short.parseShort(next());
            }
    
        }
    }