#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define Ans(f, y, n) if(f) cout << y << endl; else cout << n << endl;
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i, v.size()){ cout << v[i] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i, m.size()){ REP(j, m[i].size()){ cout << m[i][j] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

template<typename T> void readv(vector<T> &a){ REP(i, a.size()) cin >> a[i]; }
void readv_m1(vector<int> &a){ REP(i, a.size()){cin >> a[i]; a[i]--;} }

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};

const int mod = 1000000007;
//const int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod

template<long long MOD>
struct ModInt{

    using ll = long long;
    ll val;

    void setval(ll v) { val = v % MOD; };
    ModInt(): val(0) {}
    ModInt(ll v) { setval(v); };

    ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
    ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
    ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
    ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt operator+=(const ModInt &x) { return *this = *this + x; };
    ModInt operator-=(const ModInt &x) { return *this = *this - x; };
    ModInt operator*=(const ModInt &x) { return *this = *this * x; };
    ModInt operator/=(const ModInt &x) { return *this = *this / x; };

    friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
    friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }

    ModInt pow(ll n) const {
        ModInt a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            a = a * a;
            if((n >> i) & 1) a *= (*this); 
        }
        return a;
    }
    ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination{

    vector<mint> fact, invfact;

    Combination(int N){
        fact = vector<mint>({mint(1)});
        invfact = vector<mint>({mint(1)});
        fact_initialize(N);
    }

    void fact_initialize(int N){
        int i0 = fact.size();
        if(i0 >= N + 1) return;
        fact.resize(N + 1);
        invfact.resize(N + 1);
        for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
        invfact[N] = (mint)1 / fact[N];
        for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); 
    }

    mint nCr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[r] * invfact[n - r];
    }

    mint nPr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[n - r];
    }

};

struct edge{int to, cost;};

class Graph
{
public:
    int N;
    vector<vector<edge>> G;

    Graph(int N): N(N){
        G = vector<vector<edge>>(N, vector<edge>(0));
    }

    void add_edge(int from, int to, int cost = 0){
        G[from].push_back(edge({to, cost}));
    }

    void add_edge2(int v1, int v2, int cost = 0){
        add_edge(v1, v2, cost);
        add_edge(v2, v1, cost);
    }

    int dfs(int v, int to, int b = -1, int use = 0){
        if(v == to) return use;
        for(auto e: G[v]) if(e.to != b){
            int res = dfs(e.to, to, v, use ^ bit(e.cost));
            if(res != -1) return res;
        }
        return -1;
    }

};

signed main(){

    int N, M; cin >> N >> M;
    vec a(M), b(M);
    Graph G(N);
    REP(i, M){
        cin >> a[i] >> b[i];
        a[i]--; b[i]--;
        if(i < N - 1) G.add_edge2(a[i], b[i], i);
    }
    
    mat zeta(N, vec(bit(N - 1), 0));
    vec S(bit(N - 1), 0);
    REP(i, M){
        zeta[0][G.dfs(a[i], b[i])]++;
    }
    REP(i, N - 1){
        REP(j, bit(N - 1)){
            zeta[i + 1][j] += zeta[i][j];
            if((j >> i) & 1) zeta[i + 1][j] += zeta[i][j ^ bit(i)]; 
        }
    }
    REP(i, bit(N - 1)) S[i] = zeta[N - 1][i];
    //mdebug(zeta);
    //vdebug(S);
    
    mat dp(bit(N - 1)), dq(bit(N - 1));
    dp[0] = vec({1});
    dq[0] = vec({0});
    
    FOR(i, 1, bit(N - 1)){
        dp[i] = vec(S[i] + 1, 0);
        dq[i] = vec(S[i] + 1, 0);
        REP(j, N - 1) if((i >> j) & 1){
            int i0 = i ^ bit(j);
            int n = __builtin_popcountll(i0);

            FOR(k, n, S[i0] + 1){
                dp[i][k + 1] += dp[i0][k];
                dq[i][k + 1] += dq[i0][k] + dp[i0][k] * (k + 1);
            }

        }
        int n = __builtin_popcountll(i);
        dp[i][n] %= mod;
        dq[i][n] %= mod;
        FOR(k, n, S[i]){
            dp[i][k + 1] += dp[i][k] * (S[i] - k);
            dq[i][k + 1] += dq[i][k] * (S[i] - k);
            dp[i][k + 1] %= mod;
            dq[i][k + 1] %= mod;
        }
        
    }
    //mdebug(dp);
    //mdebug(dq);
    int ans = dq[bit(N - 1) - 1][M];
    cout << ans << endl;

    return 0;
}


Measured memory_bytes: 559484