We have an undirected weighted graph with N vertices and M edges. The i-th edge in the graph connects Vertex U_i and Vertex V_i, and has a weight of W_i. Additionally, you are given an integer X.

Find the number of ways to paint each edge in this graph either white or black such that the following condition is met, modulo 10^9 + 7:

* The graph has a spanning tree that contains both an edge painted white and an edge painted black. Furthermore, among such spanning trees, the one with the smallest weight has a weight of X.



Here, the weight of a spanning tree is the sum of the weights of the edges contained in the spanning tree.

Constraints

* 1 \leq N \leq 1 000
* 1 \leq M \leq 2 000
* 1 \leq U_i, V_i \leq N (1 \leq i \leq M)
* 1 \leq W_i \leq 10^9 (1 \leq i \leq M)
* If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).
* U_i \neq V_i (1 \leq i \leq M)
* The given graph is connected.
* 1 \leq X \leq 10^{12}
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N M
X
U_1 V_1 W_1
U_2 V_2 W_2
:
U_M V_M W_M


Output

Print the answer.

Examples

Input

3 3
2
1 2 1
2 3 1
3 1 1


Output

6


Input

3 3
3
1 2 1
2 3 1
3 1 2


Output

2


Input

5 4
1
1 2 3
1 3 3
2 4 6
2 5 8


Output

0


Input

8 10
49
4 6 10
8 4 11
5 8 9
1 8 10
3 8 128773450
7 8 10
4 2 4
3 4 1
3 1 13
5 2 2


Output

4
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.TreeMap;

public class Main {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		MyInput in = new MyInput(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static long LINF = 1L << 55;
	static long MOD = 1000000007;
	static int[] mh4 = { 0, -1, 1, 0 };
	static int[] mw4 = { -1, 0, 0, 1 };
	static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
	static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

	static class TaskX {

		int n, m;
		T[] T;
		long x;
		public void solve(int testNumber, MyInput in, PrintWriter out) {

			n = in.nextInt(); m = in.nextInt();
			x = in.nextLong();
			T = new T[m];
			for (int i = 0; i < m; i++) {
				int u = in.nextInt()-1, v = in.nextInt()-1;
				long w = in.nextLong();
				T[i] = new T(u, v, w);
			}

			Arrays.sort(T);

			TreeMap<Long, Long> map = new TreeMap<>();
			for (int i = 0; i < m; i++) {
				long cost = kruskal(i);
				map.merge(cost, 1L, Long::sum);
			}

			long less = 0, equal = 0;
			for (long key : map.keySet()) {
				if (key < x) less += map.get(key);
				if (key <= x) equal += map.get(key);
			}

			long ans = (MOD + f(less) - f(equal)) % MOD;
			out.println(ans);

		}

		long f(long cnt) {
			long ret = 0;
			if (cnt == 0) {
				ret = power(2, m, MOD);
			} else {
				ret = power(2, m - cnt + 1, MOD);
			}
			return ret;
		}

		long power(long a, long e, long modP) {
			long ret = 1;
			for (; e > 0; e /= 2) {
				if (e % 2 != 0) {
					ret = (ret * a) % modP;
				}
				a = (a * a) % modP;
			}
			return ret;
		}

		long kruskal(int i) {

			long ret = 0;
			UnionFind uf = new UnionFind(n);
			uf.union(T[i].s, T[i].t);
			ret += T[i].cost;

			for (int j = 0; j < m; j++) {
				if (uf.same(T[j].s, T[j].t)) continue;
				uf.union(T[j].s, T[j].t);
				ret += T[j].cost;
			}

			return ret;
		}

		class UnionFind {
			int[] data;

			public UnionFind(int size) {
				data = new int[size];
				clear();
			}

			public void clear() {
				Arrays.fill(data, -1);
			}

			public int root(int x) {
				return data[x] < 0 ? x : (data[x] = root(data[x]));
			}

			public void union(int x, int y) {
				x = root(x);
				y = root(y);

				if (x != y) {
					if (data[y] > data[x]) {
						final int t = x;
						x = y;
						y = t;
					}

					data[x] += data[y];
					data[y] = x;
				}
			}

			boolean same(int x, int y) {
				return root(x) == root(y);
			}

			public int size(int x) {
				return -data[root(x)];
			}
		}

		class T implements Comparable<T> {
			int s, t;
			long cost;

			public T(int s, int t, long cost) {
				super();
				this.s = s;
				this.t = t;
				this.cost = cost;
			}

			@Override
			public int compareTo(T o) {
				return Long.compare(this.cost, o.cost);
			}
		}
	}

	static class MyInput {
		private final BufferedReader in;
		private static int pos;
		private static int readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500 * 8 * 2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for (int i = 0; i < 10; i++) {
				isDigit['0' + i] = true;
			}
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public MyInput(InputStream is) {
			in = new BufferedReader(new InputStreamReader(is));
		}

		public int read() {
			if (pos >= readLen) {
				pos = 0;
				try {
					readLen = in.read(buffer);
				} catch (IOException e) {
					throw new RuntimeException();
				}
				if (readLen <= 0) {
					throw new MyInput.EndOfFileRuntimeException();
				}
			}
			return buffer[pos++];
		}

		public int nextInt() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			int ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public long nextLong() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			long ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public char nextChar() {
			while (true) {
				final int c = read();
				if (!isSpace[c]) {
					return (char) c;
				}
			}
		}

		public String nextString() {
			return new String(nextChars());
		}

		public char[] nextChars() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public char[][] next2DChars(int h, int w) {
			char[][] s = new char[h][w];
			for (int i = 0; i < h; i++) {
				s[i] = nextChars();
			}
			return s;
		}

		int reads(int len, boolean[] accept) {
			try {
				while (true) {
					final int c = read();
					if (accept[c]) {
						break;
					}
					if (str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					str[len++] = (char) c;
				}
			} catch (MyInput.EndOfFileRuntimeException e) {
			}
			return len;
		}

		public int[] nextIntArray(final int n) {
			final int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[] nextIntArray1Index(final int n) {
			final int[] res = new int[n + 1];
			for (int i = 1; i < n + 1; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[] nextIntArrayDec(final int n) {
			final int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt() - 1;
			}
			return res;
		}

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

		public long[] nextLongArray1Index(final int n) {
			final long[] res = new long[n + 1];
			for (int i = 1; i < n + 1; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public long[] nextLongArrayDec(final int n) {
			final long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong() - 1;
			}
			return res;
		}

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

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

		static class EndOfFileRuntimeException extends RuntimeException {
		}

	}

}
