#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [graph1; $len:expr]) => {{ let mut g = vec![vec![]; $len]; let ab = read_value!($next, [(usize1, usize1)]); for (a, b) in ab { g[a].push(b); g[b].push(a); } g }}; ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } /// Verified by https://atcoder.jp/contests/arc093/submissions/3968098 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl ::std::fmt::Debug for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { let (mut a, mut b, _) = red(self.x, M::m()); if b < 0 { a = -a; b = -b; } write!(f, "{}/{}", a, b) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } // Finds the simplest fraction x/y congruent to r mod p. // The return value (x, y, z) satisfies x = y * r + z * p. fn red(r: i64, p: i64) -> (i64, i64, i64) { if r.abs() <= 10000 { return (r, 1, 0); } let mut nxt_r = p % r; let mut q = p / r; if 2 * nxt_r >= r { nxt_r -= r; q += 1; } if 2 * nxt_r <= -r { nxt_r += r; q -= 1; } let (x, z, y) = red(nxt_r, r); (x, y - q * z, z) } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 1_000_000_007; define_mod!(P, MOD); type ModInt = mod_int::ModInt

; /// Rerooting. /// Verified by: ABC160-F /// (https://atcoder.jp/contests/abc160/submissions/11378396) /// CF627-3F /// (https://codeforces.com/contest/1324/submission/75037092) /// f: merge /// d: deepen (adds a node to a collection of child nodes) struct Reroot { g: Vec>, zero: T, dp1: Vec, dp2: Vec, dp: Vec, ch: Vec>, acc_l: Vec>, acc_r: Vec>, } impl Reroot { pub fn new(g: &[Vec], zero: T) -> Reroot { let n = g.len(); Reroot { g: g.to_vec(), zero: zero.clone(), dp1: vec![zero.clone(); n], dp2: vec![zero.clone(); n], dp: vec![zero.clone(); n], ch: vec![vec![]; n], acc_l: vec![vec![]; n], acc_r: vec![vec![]; n], } } // TODO include f in struct pub fn do_comp T, D: FnMut(T, usize) -> T>( &mut self, mut f: F, mut d: D, ) { let n = self.g.len(); Self::dfs1(0, n, &self.g, &mut self.dp1, &mut self.ch, &mut self.acc_l, &mut self.acc_r, &self.zero, &mut f, &mut d); Self::dfs2(0, &self.ch, &self.dp1, &mut self.dp2, self.zero.clone(), &self.acc_l, &self.acc_r, &self.zero, &mut f, &mut d); self.dp[0] = self.dp1[0].clone(); for i in 1..n { self.dp[i] = d(f(&self.acc_r[i][0], &self.dp2[i]), i); } } fn dfs1 T, D: FnMut(T, usize) -> T>( v: usize, par: usize, g: &[Vec], dp1: &mut [T], ch: &mut [Vec], acc_l: &mut [Vec], acc_r: &mut [Vec], zero: &T, f: &mut F, d: &mut D, ) { let mut ary = vec![]; let mut mych = vec![]; for &w in &g[v] { if w == par { continue; } mych.push(w); Self::dfs1(w, v, g, dp1, ch, acc_l, acc_r, zero, f, d); ary.push(dp1[w].clone()); } let m = ary.len(); acc_l[v] = vec![zero.clone(); m + 1]; acc_r[v] = vec![zero.clone(); m + 1]; for i in 0..m { let val = f(&acc_l[v][i], &ary[i]); acc_l[v][i + 1] = val; } for i in (0..m).rev() { let val = f(&acc_r[v][i + 1], &ary[i]); acc_r[v][i] = val; } ch[v] = mych; dp1[v] = d(acc_r[v][0].clone(), v); } fn dfs2 T, D: FnMut(T, usize) -> T>( v: usize, ch: &[Vec], dp1: &[T], dp2: &mut [T], passed: T, acc_l: &[Vec], acc_r: &[Vec], zero: &T, f: &mut F, d: &mut D, ) { dp2[v] = passed.clone(); for i in 0..ch[v].len() { let w = ch[v][i]; let leave_one = f(&acc_l[v][i], &acc_r[v][i + 1]); Self::dfs2(w, ch, dp1, dp2, d(f(&leave_one, &passed), v), acc_l, acc_r, zero, f, d); } } } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } input! { n: usize, k: usize, ab: [(usize1, usize1); n - 1], } let mut g = vec![vec![]; n]; for &(a, b) in &ab { g[a].push(b); g[b].push(a); } let zero = vec![ModInt::new(1); k]; let mut reroot = Reroot::new(&g, zero); let f = |a: &Vec, b: &Vec| { let mut c = vec![ModInt::new(0); a.len()]; for i in 0..a.len() { c[i] = a[i] * b[i]; } c }; let d = |mut a: Vec, _v: usize| { for i in 0..a.len() - 1 { let val = a[i]; a[i + 1] += val; } a }; reroot.do_comp(f, d); let mut tot = ModInt::new(0); for i in 0..n { tot += reroot.dp[i][k - 1]; } for v in 1..n { for j in 0..k { let par = reroot.dp2[v][j] - if j == 0 { ModInt::new(0) } else { reroot.dp2[v][j - 1] }; let ch = reroot.dp1[v][j] - if j == 0 { ModInt::new(0) } else { reroot.dp1[v][j - 1] }; tot -= par * ch; } } puts!("{}\n", tot); } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }