import java.io.OutputStream; import java.io.IOException; import java.io.InputStream; import java.util.Arrays; import java.nio.ByteBuffer; import java.util.ArrayList; import java.nio.charset.Charset; import java.util.NoSuchElementException; import java.io.OutputStream; import java.nio.CharBuffer; import java.io.IOException; import java.nio.charset.CharsetDecoder; import java.lang.reflect.Field; import java.nio.charset.StandardCharsets; import java.io.UncheckedIOException; import java.util.Objects; import java.util.List; import java.io.Writer; import java.io.InputStream; /** * Built using CHelper reloaded plug-in * Actual solution is at the top * * @author mikit */ public class Main { public static void main(String[] args) { InputStream inputStream = System.in; OutputStream outputStream = System.out; LightScanner2 in = new LightScanner2(inputStream); LightWriter2 out = new LightWriter2(outputStream); No1207X solver = new No1207X(); solver.solve(1, in, out); out.close(); } static class No1207X { private static final int MOD = (int) 1e9 + 7; public void solve(int testNumber, LightScanner2 in, LightWriter2 out) { ModMath mod = new ModMath(MOD); int n = in.ints(), m = in.ints(), b = in.ints(); No1207X.Node[] nodes = new No1207X.Node[n]; for (int i = 0; i < n; i++) nodes[i] = new No1207X.Node(); IntUnionFind uf = new IntUnionFind(n); for (int i = 0; i < m; i++) { int x = in.ints() - 1, y = in.ints() - 1, z = in.ints(); if (uf.find(x) == uf.find(y)) continue; uf.union(x, y); nodes[x].edges.add(new No1207X.Edge(nodes[y], mod.pow(b, z))); nodes[y].edges.add(new No1207X.Edge(nodes[x], mod.pow(b, z))); } nodes[0].dfs(null); long ans = 0; for (No1207X.Node node : nodes) { for (No1207X.Edge edge : node.edges) { if (edge.size == -1) continue; //System.out.println(edge.size + " : " + edge.cost); long p = edge.size * (long) (n - edge.size) % MOD; p *= edge.cost; ans += p % MOD; } ans %= MOD; } out.ans(ans).ln(); } private static class Node { List edges = new ArrayList<>(); int size = -1; void dfs(No1207X.Node from) { size = 1; for (No1207X.Edge edge : edges) { if (edge.dest == from) continue; edge.dest.dfs(this); edge.size = edge.dest.size; size += edge.dest.size; } } } private static class Edge { No1207X.Node dest; long cost; int size = -1; Edge(No1207X.Node dest, long cost) { this.dest = dest; this.cost = cost; } } } static class LightScanner2 extends LightScannerAdapter { private static final int BUF_SIZE = 32 * 1024; private final InputStream stream; private final byte[] buf = new byte[BUF_SIZE]; private int ptr; private int len; public LightScanner2(InputStream stream) { this.stream = stream; } private int read() { if (ptr < len) return buf[ptr++]; try { ptr = 0; len = stream.read(buf); } catch (IOException ex) { throw new UncheckedIOException(ex); } if (len == -1) return -1; return buf[ptr++]; } private void skip() { int b; while (isTokenSeparator(b = read()) && b != -1) ; if (b == -1) throw new NoSuchElementException("EOF"); ptr--; } public int ints() { long x = longs(); if (x < Integer.MIN_VALUE || Integer.MAX_VALUE < x) throw new NumberFormatException("Overflow"); return (int) x; } public long longs() { skip(); int b = read(); boolean negate; if (b == '-') { negate = true; b = read(); } else negate = false; long x = 0; for (; !isTokenSeparator(b); b = read()) { if ('0' <= b && b <= '9') x = x * 10 + b - '0'; else throw new NumberFormatException("Unexpected character '" + b + "'"); } return negate ? -x : x; } public void close() { try { stream.close(); } catch (IOException e) { throw new UncheckedIOException(e); } } private static boolean isTokenSeparator(int b) { return b < 33 || 126 < b; } } static interface Verified { } static class ModMath { private static final int DEFAULT_MOD = 1_000_000_007; private final long mod; public ModMath(long mod, boolean unsafe) { /*if (!unsafe && !IntMath.isPrime(mod)) { throw new RuntimeException("This class is designed for primes!"); }*/ this.mod = mod; } public ModMath(long mod) { this(mod, false); } public ModMath() { this(DEFAULT_MOD, true); } public long mod(long x) { x %= mod; return x < 0 ? x + mod : x; } public long inv(long x) { //return pow(x, mod - 2); return mod(LongEuclidSolver.solve(x, mod).x); } public long pow(long x, long y) { y %= (mod - 1); if (y < 0) { return pow(inv(x), -y); } else if (y == 0) { return 1; } else if (y % 2 == 0) { long z = pow(x, y / 2); return (z * z) % mod; } else { return (x % mod) * pow(x, y - 1) % mod; } } } static class Vec3i implements Comparable { public int x; public int y; public int z; public Vec3i(int x, int y, int z) { this.x = x; this.y = y; this.z = z; } public boolean equals(Object o) { if (this == o) return true; if (o == null || getClass() != o.getClass()) return false; Vec3i vec3i = (Vec3i) o; return x == vec3i.x && y == vec3i.y && z == vec3i.z; } public int hashCode() { return Objects.hash(x, y, z); } public String toString() { return "(" + x + ", " + y + ", " + z + ")"; } public int compareTo(Vec3i o) { if (x == o.x) { if (y == o.y) { return Integer.compare(z, o.z); } return Integer.compare(y, o.z); } return Integer.compare(x, o.x); } } static class LongEuclidSolver { private LongEuclidSolver() { } public static Vec3l solve(long a, long b) { LongEuclidSolver.ReferenceLong p = new LongEuclidSolver.ReferenceLong(), q = new LongEuclidSolver.ReferenceLong(); long d = solve(a, b, p, q); return new Vec3l(p.val, q.val, d); } private static long solve(long a, long b, LongEuclidSolver.ReferenceLong p, LongEuclidSolver.ReferenceLong q) { if (b == 0) { p.val = 1; q.val = 0; return a; } else { long d = solve(b, a % b, q, p); q.val -= (a / b) * p.val; return d; } } private static class ReferenceLong { private long val; } } static class LightWriter2 implements AutoCloseable { private static final int BUF_SIZE = 32 * 1024; private static final int BUF_THRESHOLD = 1024; private final OutputStream out; private final byte[] buf = new byte[BUF_SIZE]; private int ptr; private final Field fastStringAccess; private boolean autoflush = false; private boolean breaked = true; public LightWriter2(OutputStream out) { this.out = out; Field f; try { f = String.class.getDeclaredField("value"); f.setAccessible(true); if (f.getType() != byte[].class) f = null; } catch (ReflectiveOperationException ignored) { f = null; } this.fastStringAccess = f; } public LightWriter2(Writer out) { this.out = new LightWriter2.WriterOutputStream(out); this.fastStringAccess = null; } private void allocate(int n) { if (ptr + n <= BUF_SIZE) return; try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException ex) { throw new UncheckedIOException(ex); } if (BUF_SIZE < n) throw new IllegalArgumentException("Internal buffer exceeded"); } public void close() { try { out.write(buf, 0, ptr); ptr = 0; out.flush(); out.close(); } catch (IOException ex) { throw new UncheckedIOException(ex); } } public LightWriter2 print(char c) { allocate(1); buf[ptr++] = (byte) c; breaked = false; return this; } public LightWriter2 print(String s) { byte[] bytes; if (this.fastStringAccess == null) bytes = s.getBytes(); else { try { bytes = (byte[]) fastStringAccess.get(s); } catch (IllegalAccessException ignored) { bytes = s.getBytes(); } } int n = bytes.length; if (n <= BUF_THRESHOLD) { allocate(n); System.arraycopy(bytes, 0, buf, ptr, n); ptr += n; return this; } try { out.write(buf, 0, ptr); ptr = 0; out.write(bytes); out.flush(); } catch (IOException ex) { throw new UncheckedIOException(ex); } return this; } public LightWriter2 ans(long l) { if (!breaked) { print(' '); } if (l == 0) return print('0'); if (l < 0) { print('-'); l = -l; } int n = 0; long t = l; while (t > 0) { t /= 10; n++; } allocate(n); for (int i = 1; i <= n; i++) { buf[ptr + n - i] = (byte) (l % 10 + '0'); l /= 10; } ptr += n; return this; } public LightWriter2 ln() { print(System.lineSeparator()); breaked = true; if (autoflush) { try { out.flush(); } catch (IOException ex) { throw new UncheckedIOException(ex); } } return this; } private static class WriterOutputStream extends OutputStream { final Writer writer; final CharsetDecoder decoder; WriterOutputStream(Writer writer) { this.writer = writer; this.decoder = StandardCharsets.UTF_8.newDecoder(); } public void write(int b) throws IOException { writer.write(b); } public void write(byte[] b) throws IOException { writer.write(decoder.decode(ByteBuffer.wrap(b)).array()); } public void write(byte[] b, int off, int len) throws IOException { writer.write(decoder.decode(ByteBuffer.wrap(b, off, len)).array()); } public void flush() throws IOException { writer.flush(); } public void close() throws IOException { writer.close(); } } } static final class IntUnionFind { private int groups; private final int[] nodes; private final int[] rank; public IntUnionFind(int n) { groups = n; nodes = new int[n]; Arrays.fill(nodes, -1); rank = new int[n]; } public int find(int i) { int ans = nodes[i]; if (ans < 0) { return i; } else { return nodes[i] = find(ans); } } public boolean union(int x, int y) { x = find(x); y = find(y); if (x == y) { return false; } else if (rank[x] < rank[y]) { nodes[y] += nodes[x]; nodes[x] = y; } else if (rank[x] == rank[y]) { rank[x]++; nodes[x] += nodes[y]; nodes[y] = x; } else { nodes[x] += nodes[y]; nodes[y] = x; } groups--; return true; } } static class Vec3l implements Comparable { public long x; public long y; public long z; public Vec3l(long x, long y, long z) { this.x = x; this.y = y; this.z = z; } public boolean equals(Object o) { if (this == o) return true; if (o == null || getClass() != o.getClass()) return false; Vec3i vec3i = (Vec3i) o; return x == vec3i.x && y == vec3i.y && z == vec3i.z; } public int hashCode() { return Objects.hash(x, y, z); } public String toString() { return "(" + x + ", " + y + ", " + z + ")"; } public int compareTo(Vec3l o) { if (x == o.x) { if (y == o.y) { return Long.compare(z, o.z); } return Long.compare(y, o.z); } return Long.compare(x, o.x); } } static abstract class LightScannerAdapter implements AutoCloseable { public abstract void close(); } }