#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

struct Comb {
    div: usize,
    g1: Vec<usize>,
    g2: Vec<usize>,
}
impl Comb {
#[allow(dead_code)]
    fn new(nmax: usize) -> Self {
        let mut g1 = vec![1; nmax + 1];
        let mut g2 = vec![1; nmax + 1];
        let mut inv = vec![0; nmax + 1];
        inv[1] = 1;
        let div = 1000000007;
        for i in 2..(nmax + 1) {
            g1[i] = g1[i - 1] * i % div;
            inv[i] = div - (inv[div % i] * (div / i)) % div;
            g2[i] = (g2[i - 1] * inv[i]) % div;
        }
        Comb {
            div: div,
            g1: g1,
            g2: g2,
        }
    }
#[allow(dead_code)]
    fn compute(&self, n: usize, k: usize) -> usize {
        (((self.g1[n] * self.g2[k]) % self.div) * self.g2[n - k]) % self.div
    }
#[allow(dead_code)]
    fn compute_dupc(&self, n: usize, k: usize) -> usize {
        self.compute(n + k - 1, n - 1)
    }
#[allow(dead_code)]
    fn compute_perm(&self, n: usize, k: usize) -> usize {
        (self.g1[n] * self.g2[n - k]) % self.div
    }
}

fn solve() {
    let (n,k) = get!(usize, usize);
    let ab = get!(usize, usize;n-1);

    let mo = 1_000_000_007;
    let comb = Comb::new(k);
    let mut nodes = vec![Vec::new(); n+1];
    for (a,b) in ab {
        nodes[a].push(b);
        nodes[b].push(a);
    }

    if k == 1 {
        if n > 1 {
            println!("0");
        } else {
            println!("{}", k);
        }
        return;
    } else if k == 2 {
        if n > 2 {
            println!("0");
        } else if n == 2{
            println!("{}", k*(k-1));
        } else {
            println!("{}", k);
        }
        return;
    }
    if nodes[1].len()+1 > k {
        println!("0");
        return;
    }
    let mut queue = VecDeque::new();
    let mut visited = vec![false; n+1];
    visited[1] = true;
    let mut res = 1usize;
    for &node in &nodes[1] {
        queue.push_back(node);
        visited[node] = true;
    }
    res *= comb.compute_perm(k, nodes[1].len()+1);
    
    while let Some(node) = queue.pop_front() {
        if k < nodes[node].len()+1 {
            res = 0;
            continue;
        }
        res *= comb.compute_perm(k-2, nodes[node].len()-1);
        res %= mo;
        for &next in &nodes[node] {
            if visited[next] {
                continue;
            }
            visited[next] = true;
            queue.push_back(next);
        }
    }
    println!("{}", res);
}


Measured memory_bytes: 18812