#![allow(unused_imports, unused_macros)] use kyoproio::*; use std::{ collections::*, io::{self, prelude::*}, iter, mem::{replace, swap}, }; fn main() -> io::Result<()> { std::thread::Builder::new() .stack_size(64 * 1024 * 1024) .spawn(|| { run( KInput::new(io::stdin().lock()), io::BufWriter::new(io::stdout().lock()), ) })? .join() .unwrap(); Ok(()) } fn run(mut kin: I, mut out: O) { macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+).unwrap(); }; } macro_rules! outputln { ($($args:expr),+) => { output!($($args),+); outputln!(); }; () => { output!("\n"); if cfg!(debug_assertions) { out.flush().unwrap(); } } } let (n, m, x): (usize, usize, i64) = kin.input(); let mut es: Vec<(usize, usize, i64)> = kin.seq(m); es.sort_by_key(|(_, _, z)| *z); let mut uf = UnionFind::new(n + 1); let mut g = vec![Vec::new(); n + 1]; for (u, v, z) in es { if !uf.is_same(u, v) { uf.unite(u, v); g[u].push((v, z)); g[v].push((u, z)); } } X.set(x); G.set(g); let ans = f(1, 0).1; outputln!("{}", ans); } const P: i64 = 1e9 as i64 + 7; static X: OnceInit = OnceInit::new(); static G: OnceInit>> = OnceInit::new(); fn f(u: usize, p: usize) -> (usize, i64) { let mut size = 0; let mut dist = 0; for &(v, z) in &G[u] { if v != p { let (s, d) = f(v, u); size += s; let t = G.len() - 1 - s; dist = (dist + d + mod_pow(*X, z, P) * s as i64 % P * t as i64) % P; } } (size + 1, dist) } pub fn mod_pow(mut a: i64, mut b: i64, m: i64) -> i64 { let mut y = 1; while b > 0 { if b & 1 == 1 { y = y * a % m; } a = a * a % m; b >>= 1; } y } pub struct UnionFind { p: Vec, } impl UnionFind { pub fn new(n: usize) -> Self { Self { p: vec![-1; n] } } pub fn root(&self, mut u: usize) -> usize { while self.p[u] >= 0 { u = self.p[u] as usize; } u } pub fn size(&self, u: usize) -> usize { (-self.p[self.root(u)]) as usize } pub fn unite(&mut self, u: usize, v: usize) -> bool { let mut u = self.root(u); let mut v = self.root(v); if u == v { return false; } if self.p[u] > self.p[v] { swap(&mut u, &mut v); } self.p[u] += self.p[v]; self.p[v] = u as isize; true } pub fn is_same(&self, u: usize, v: usize) -> bool { self.root(u) == self.root(v) } } use std::{cell::UnsafeCell, sync::Once}; pub struct OnceInit { value: UnsafeCell>, once: Once, } unsafe impl Sync for OnceInit {} impl OnceInit { pub const fn new() -> Self { Self { value: UnsafeCell::new(None), once: Once::new(), } } pub fn set(&self, value: T) { self.once.call_once(|| unsafe { let v = &mut *self.value.get(); if v.is_none() { *v = Some(value); } }); } pub fn get(&self) -> Option<&T> { unsafe { (*self.value.get()).as_ref() } } } impl std::ops::Deref for OnceInit { type Target = T; fn deref(&self) -> &Self::Target { self.get().unwrap() } } // ----------------------------------------------------------------------------- pub mod kyoproio { use std::io::prelude::*; pub trait Input { fn str(&mut self) -> &str; fn input(&mut self) -> T { T::input(self) } fn iter(&mut self) -> Iter { Iter(self, std::marker::PhantomData) } fn seq>(&mut self, n: usize) -> B { self.iter().take(n).collect() } } pub struct KInput { src: R, buf: String, pos: usize, } impl KInput { pub fn new(src: R) -> Self { Self { src, buf: String::with_capacity(1 << 12), pos: 0, } } } impl Input for KInput { fn str(&mut self) -> &str { loop { if self.pos >= self.buf.len() { self.pos = 0; self.buf.clear(); if self.src.read_line(&mut self.buf).expect("io error") == 0 { return &self.buf; } } let range = self.pos ..self.buf[self.pos..] .find(|c: char| c.is_ascii_whitespace()) .map(|i| i + self.pos) .unwrap_or_else(|| self.buf.len()); self.pos = range.end + 1; if range.end > range.start { return &self.buf[range]; } } } } pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>); impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> { type Item = T; fn next(&mut self) -> Option { Some(self.0.input()) } } pub trait InputParse: Sized { fn input(src: &mut I) -> Self; } impl InputParse for Vec { fn input(src: &mut I) -> Self { src.str().as_bytes().to_owned() } } macro_rules! from_str_impl { { $($T:ty)* } => { $(impl InputParse for $T { fn input(src: &mut I) -> Self { src.str().parse::<$T>().expect("parse error") } })* } } from_str_impl! { String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128 } macro_rules! tuple_impl { ($H:ident $($T:ident)*) => { impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) { fn input(src: &mut I) -> Self { ($H::input(src), $($T::input(src)),*) } } tuple_impl!($($T)*); }; () => {} } tuple_impl!(A B C D E F G); #[macro_export] macro_rules! kdbg { ($($v:expr),*) => { if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) } } } }