#![allow(unused_imports)] #![allow(non_snake_case, unused)] use std::cmp::*; use std::collections::*; use std::ops::*; // https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254 より macro_rules! eprint { ($($t:tt)*) => {{ use ::std::io::Write; let _ = write!(::std::io::stderr(), $($t)*); }}; } macro_rules! eprintln { () => { eprintln!(""); }; ($($t:tt)*) => {{ use ::std::io::Write; let _ = writeln!(::std::io::stderr(), $($t)*); }}; } macro_rules! dbg { ($v:expr) => {{ let val = $v; eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val); val }} } macro_rules! mat { ($($e:expr),*) => { Vec::from(vec![$($e),*]) }; ($($e:expr,)*) => { Vec::from(vec![$($e),*]) }; ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) }; ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) }; } macro_rules! ok { ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => { $a$([$i])*.$f($($t),*) }; ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { { let t = $e; ok!($a$([$i])*.$f($($es),*)$(@$t)*@t) } }; } pub fn readln() -> String { let mut line = String::new(); ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e)); line } macro_rules! read { ($($t:tt),*; $n:expr) => {{ let stdin = ::std::io::stdin(); let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| { let line = line.unwrap(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }).collect::>(); ret }}; ($($t:tt),*) => {{ let line = readln(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }}; } macro_rules! _read { ($it:ident; [char]) => { _read!($it; String).chars().collect::>() }; ($it:ident; [u8]) => { Vec::from(_read!($it; String).into_bytes()) }; ($it:ident; usize1) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::().unwrap_or_else(|e| panic!("{}", e)) - 1 }; ($it:ident; [usize1]) => { $it.map(|s| s.parse::().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::>() }; ($it:ident; [$t:ty]) => { $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::>() }; ($it:ident; $t:ty) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e)) }; ($it:ident; $($t:tt),+) => { ($(_read!($it; $t)),*) }; } pub fn main() { let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join(); } // const MOD: usize = 998244353; // const MOD: usize = 1_000_000_007; const INF: i64 = std::i64::MAX/100; // https://yukicoder.me/submissions/585145 より // ---------- begin ModInt ---------- mod modint { #[allow(dead_code)] pub struct Mod; impl ConstantModulo for Mod { const MOD: u32 = 1_000_000_007; } #[allow(dead_code)] pub struct StaticMod; static mut STATIC_MOD: u32 = 0; impl Modulo for StaticMod { fn modulo() -> u32 { unsafe { STATIC_MOD } } } #[allow(dead_code)] impl StaticMod { pub fn set_modulo(p: u32) { unsafe { STATIC_MOD = p; } } } use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub trait ConstantModulo { const MOD: u32; } impl Modulo for T where T: ConstantModulo, { fn modulo() -> u32 { T::MOD } } pub struct ModInt(pub u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { ModInt::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut d = self.0 + rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut d = T::modulo() + self.0 - rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; ModInt::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.0 == 0 { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl ModInt { pub fn new_unchecked(d: u32) -> Self { ModInt(d, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } #[allow(dead_code)] impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } pub fn pow(&self, mut n: u64) -> Self { let mut t = Self::one(); let mut s = *self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(&self) -> Self { assert!(self.0 != 0); self.pow(T::modulo() as u64 - 2) } } #[allow(dead_code)] pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 { let mut t = 1 % m; let mut s = r % m; while n > 0 { if n & 1 == 1 { t = t * s % m; } s = s * s % m; n >>= 1; } t } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- mod precalc { use super::modint::*; #[allow(dead_code)] pub struct Precalc { inv: Vec>, fact: Vec>, ifact: Vec>, } #[allow(dead_code)] impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..(n + 1) { fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32); } ifact[n] = fact[n].inv(); if n > 0 { inv[n] = ifact[n] * fact[n - 1]; } for i in (1..n).rev() { ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32); inv[i] = ifact[i] * fact[i - 1]; } Precalc { inv: inv, fact: fact, ifact: ifact, } } pub fn inv(&self, n: usize) -> ModInt { assert!(n > 0); self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn perm(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[n - k] } pub fn comb(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } } // ---------- end Precalc ---------- use modint::*; type M = ModInt; fn solve() { let (n,c) = read!(usize,usize); let ab = read!(usize,usize;n-1); let mut edge = vec![vec![];n]; for &(a,b) in &ab { edge[a-1].push(b-1); edge[b-1].push(a-1); } let mut dp = vec![vec![M::one();10000];n]; dfs(0,n,c,&edge,&mut dp); let mut ans = M::zero(); let l = min(1+5000,c); let r = max(c as i64 -5000,l as i64+1) as usize; for i in 1..=l { ans += dp[0][i]; } ans += M::new(2).pow((n-1) as u64) * M::from(r-l-1); for i in r..=c { ans += dp[0][c-i]; } println!("{}",ans); } fn dfs(cur: usize, p: usize, c: usize, edge: &Vec>, mut dp: &mut Vec>) { for &e in &edge[cur] { if p==e { continue; } dfs(e,cur,c,&edge,&mut dp); for i in 0..9000 { let mut count = M::zero(); if i+3<=c { count += dp[e][i+3]; } if i>=4 && i-3<=c { count += dp[e][i-3]; } dp[cur][i] *= count; } } } fn run() { let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); solve(); }