const long long MOD = 1e9 + 7;

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

void dfs(int v, int par, vector<int> &h, vector<int> &edge_in, vector<int> &a, vector<int> &b)
{
    if (v == par) h[v] = 0;
    else h[v] = h[par] + 1;
    for (int i = 0; i < h.size() - 1; i++)
    {
        if (a[i] == v || b[i] == v)
        {
            int u = a[i] + b[i] - v;
            if (u != par)
            {
                edge_in[u] = i;
                dfs(u, v, h, edge_in, a, b);
            }
        }
    }
}

int mark(int v, int u, vector<int> &h, vector<int> &edge_in, vector<int> &a, vector<int> &b)
{
    int mask = 0;
    while (h[v] > h[u])
    {
        mask += 1 << edge_in[v];
        int f = a[edge_in[v]] + b[edge_in[v]] - v;
        v = f;
    }
    while (h[v] < h[u])
    {
        mask += 1 << edge_in[u];
        int f = a[edge_in[u]] + b[edge_in[u]] - u;
        u = f;
    }
    while (v != u)
    {
        mask += 1 << edge_in[v];
        int f = a[edge_in[v]] + b[edge_in[v]] - v;
        v = f;
        mask += 1 << edge_in[u];
        f = a[edge_in[u]] + b[edge_in[u]] - u;
        u = f;
    }
    return mask;
}

const int N = 206;
const int M = (1 << 19) + 2;

ll dp[M];
ll EV[M];
ll ans[M];
int on_right[M];
ll Supersigmacnk[N][N];
ll Supersigmacnkdec[N][N];
ll Supersigmacnkinc[N][N];
ll cnk[N][N];
ll fact[N];
ll rev[N];

inline ll supersigmacnkdec(ll i, ll k, ll n)
{
    ll ans = Supersigmacnk[k][n] * (i + MOD - 1) % MOD;
    ans = (ans + Supersigmacnkdec[k][n]) % MOD;
    return ans;
}

inline ll supersigmacnkinc(ll i, ll k, ll n)
{
    ll ans = Supersigmacnk[k][n] * i % MOD;
    ans = (ans + Supersigmacnkinc[k][n]) % MOD;
    return ans;
}

signed main()
{
    srand(time(NULL));
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    fact[0] = 1;
    rev[1] = 1;
    for (int i = 1; i < N; i++) fact[i] = (fact[i - 1] * i) % MOD;
    for (int i = 2; i < N; i++) rev[i] = MOD - (MOD / i) * rev[MOD % i] % MOD;
    for (int i = 0; i < N; i++)
    {
        cnk[i][0] = cnk[i][i] = 1;
        for (int j = 1; j < i; j++)
        {
            cnk[i][j] = (cnk[i - 1][j - 1] + cnk[i - 1][j]) % MOD;
        }
    }
    for (int k = 0; k < N; k++)
    {
        for (int n = k; n < N; n++)
        {
            Supersigmacnk[k][n] = ((n != k ? Supersigmacnk[k][n - 1] : 0) + cnk[n][k]) % MOD;
            Supersigmacnkdec[k][n] = ((n != k ? Supersigmacnkdec[k][n - 1] : 0) + Supersigmacnk[k][n]) % MOD;
            Supersigmacnkinc[k][n] = ((n != k ? Supersigmacnkinc[k][n - 1] : 0) + (n - k) * cnk[n][k]) % MOD;
        }
    }

    int n, m;
    cin >> n >> m;
    vector<int> a(m), b(m);
    for (int i = 0; i < m; i++)
    {
        cin >> a[i] >> b[i];
        a[i]--, b[i]--;
    }
    vector<int> h(n), edge_in(n);
    dfs(0, 0, h, edge_in, a, b);
    vector<int> suba(m);
    for (int i = n - 1; i < m; i++)
    {
        int z = mark(a[i], b[i], h, edge_in, a, b);
        suba[i] = z;
    }
    int M = 1 << (n - 1);
    {
        for (int i = n - 1; i < m; i++)
        {
            int w = M - 1 - suba[i];
            on_right[w]++;
        }
        for (int b = 0; b < n - 1; b++)
        {
            for (int i = M - 1; i >= 0; i--)
            {
                if (i & (1 << b)) continue;
                on_right[i] += on_right[i + (1 << b)];
            }
        }
        for (int mask = 1; mask < M; mask++)
        {
            on_right[mask] = m - n + 1 - on_right[mask];
            on_right[mask] += __builtin_popcount(mask) - 1;
        }
        on_right[0] = -1;
        dp[0] = 1;
        for (int mask = 1; mask < M; mask++)
        {
            ll summ_right = 0, cnt_left = 0;
            for (int p = 0; p < n - 1; p++)
            {
                if (mask & (1 << p))
                {
                    int pmask = mask - (1 << p);
                    if (pmask == 0)
                    {
                        dp[mask] = fact[on_right[mask]];
                        EV[mask] = fact[on_right[mask]];
                        ans[mask] = fact[on_right[mask]] * (m - on_right[mask]) % MOD;
                        continue;
                    }
                    int cnt = on_right[mask] - on_right[pmask] - 1;

                    ll ways = cnk[on_right[mask]][on_right[pmask] + 1] * fact[on_right[mask] - on_right[pmask] - 1] % MOD;
                    ll dpways = dp[pmask] * ways % MOD;
                    dp[mask] = (dp[mask] + dpways) % MOD;

                    ll W = fact[cnt] * dp[pmask] % MOD;
                    ll SS1 = Supersigmacnkdec[on_right[pmask]][on_right[mask] - 1];
                    cnt_left = (cnt_left + SS1 * W) % MOD;

                    ll SS2 = supersigmacnkinc(on_right[pmask] + 1, on_right[pmask], on_right[mask] - 1);
                    
                    summ_right = (summ_right + SS2 * fact[cnt] % MOD * (EV[pmask] + dp[pmask])) % MOD;
                    ll SS3 = Supersigmacnk[on_right[pmask]][on_right[mask] - 1];

                    ll SS4 = supersigmacnkinc(0, on_right[pmask], on_right[mask] - 1);
                    ans[mask] = (ans[mask] + ans[pmask] * fact[cnt] % MOD * SS3
                                 + (m - on_right[mask]) * W % MOD * SS3
                                 - EV[pmask] * fact[cnt] % MOD * SS4
                                 ) % MOD;
                    if (ans[mask] < 0) ans[mask] += MOD;
                }
            }
            if (__builtin_popcount(mask) > 1)
            {
                //cout << mask << " " << summ_right << " " << cnt_left << " " << cnt_right << "\n";
                EV[mask] = (cnt_left + summ_right) * rev[on_right[mask] + 1] % MOD;
            }
            //cout << mask << " " << dp[mask] << " " << EV[mask] << " " << ans[mask] << "\n";
        }
        //cout << dp[M - 1] << "\n";
        cout << ans[M - 1] << "\n";
    }
}

/* Note:
Check constants at the beginning of the code (MOD, INF, INFLL)
Check corner cases.
    N = 1
No def int long long for now.
Add something here.
*/


Measured memory_bytes: 19300