#[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, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    }};

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

/// 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<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // 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<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        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<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        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<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // 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<P>;
fn dfs(r: usize, v: usize, par: usize,
       u: usize, used: &mut [Vec<usize>], g: &[Vec<(usize, usize)>]) {
    used[r][v] = u;
    for &(w, idx) in &g[v] {
        if par == w { continue; }
        dfs(r, w, v, u | 1 << idx, used, g);
    }
}

// Depends on ModInt.rs
fn fact_init(w: usize) -> (Vec<ModInt>, Vec<ModInt>) {
    let mut fac = vec![ModInt::new(1); w];
    let mut invfac = vec![0.into(); w];
    for i in 1 .. w {
        fac[i] = fac[i - 1] * i as i64;
    }
    invfac[w - 1] = fac[w - 1].inv();
    for i in (0 .. w - 1).rev() {
        invfac[i] = invfac[i + 1] * (i as i64 + 1);
    }
    (fac, invfac)
}

fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }
    macro_rules! debug {
        //($($format:tt)*) => (eprintln!($($format)*));
        ($($format:tt)*) => ();
    }
    input! {
        n: usize, m: usize,
        ab: [(usize1, usize1); m],
    }
    let (fac, invfac) = fact_init(m + 2);
    let comb = |x: usize, y: usize|
    if x < y {
        ModInt::new(0)
    } else {
        fac[x] * invfac[y] * invfac[x - y]
    };
    let mut g = vec![vec![]; n];
    for i in 0..n - 1 {
        let (a, b) = ab[i];
        g[a].push((b, i));
        g[b].push((a, i));
    }
    let mut used = vec![vec![0; n]; n];
    for i in 0..n {
        dfs(i, i, n, 0, &mut used, &g);
    }
    // cnt
    let mut cnt = vec![0usize; 1 << (n - 1)];
    let mut ints = vec![0usize; 1 << (n - 1)];
    for i in 0..m {
        let (a, b) = ab[i];
        cnt[used[a][b]] += 1;
    }
    for i in 0..n - 1 {
        for bits in 0..1 << (n - 1) {
            if (bits & 1 << i) == 0 {
                cnt[bits | 1 << i] += cnt[bits];
            }
        }
    }
    for bits in 0..1 << (n - 1) {
        ints[bits] = m - cnt[(1 << (n - 1)) - 1 - bits];
    }
    debug!("cnt = {:?}", cnt);
    let mut dp1 = vec![ModInt::new(0); 1 << (n - 1)];
    let mut dp2 = vec![ModInt::new(0); 1 << (n - 1)];
    dp1[0] = ModInt::new(1);
    let full = (1 << (n - 1)) - 1;
    for bits in 0..1 << (n - 1) {
        for j in 0..n - 1 {
            if (bits & 1 << j) == 0 {
                let x = ints[bits] as i64;
                let y = ints[bits ^ 1 << j] as i64 - x - 1;

                let intercalate = ModInt::new(x + y + 1).inv();
                debug!("{} => {}", bits, intercalate * fac[m]);
                dp1[bits ^ 1 << j] += dp1[bits] * intercalate;
                let ratio = ModInt::new(x + y + 1) * ModInt::new(x + 1).inv();
                debug!("bits = {}, j = {}, x = {}, y = {}, ratio = {} / {}", bits, j, x, y, ratio * fac[m], fac[m]);
                dp2[bits ^ 1 << j] += intercalate *
                    (ratio * dp2[bits] + dp1[bits] * (bits.count_ones() as i64 + 1));
            }
        }
    }
    let mut tot = ModInt::new(0);
    for i in n - 1..m {
        let (a, b) = ab[i];
        let k = used[a][b].count_ones() as i64 + 2;
        let rem = n as i64 - 1 - (k - 2);
        debug!("k = {}, rem = {}", k, rem);
        tot += ModInt::new(rem) * ModInt::new(k).inv();
    }
    for i in 0..n - 1 {
        tot += (n - i - 1) as i64;
    }
    debug!("dp1 = {:?}", dp1);
    debug!("dp2 = {:?}", dp2);
    puts!("{}\n", fac[m] * dp2[full]);
}

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();
}


Measured memory_bytes: 24828