#include "bits/extc++.h"

using namespace std;

template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
    cerr << t;
    ((cerr << " | " << u), ...);
    cerr << endl;
}

#ifdef DEBUG
#define dbg(...)                                           \
    cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]" \
         << ": ";                                          \
    dbgh(__VA_ARGS__)
#else
#define cerr   \
    if (false) \
    cerr
#define dbg(...)
#endif

#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))

template <typename T>
ostream& operator<<(ostream& out, const vector<T>& arr) {
    out << "[";
    for (int i = 0; i < sz(arr); i++) {
        if (i) {
            out << ", ";
        }
        out << arr[i];
    }
    return out << "]";
}

bool on(int mask, int bit) {
    return (mask >> bit) & 1;
}

struct mint {
    static constexpr int MOD = 1e9 + 7;

    static int norm(long x) {
        x %= MOD;
        if (x < 0) {
            x += MOD;
        }
        return x;
    }

    static mint pow(mint base, long exp) {
        mint ans = 1;

        while (exp) {
            if (exp & 1) {
                ans *= base;
            }
            base *= base;
            exp >>= 1;
        }

        return ans;
    }

    static mint inv(mint x) {
        return mint::pow(x, MOD - 2);
    }

    int x;

    mint() : x(0) {}
    mint(long x) : x(norm(x)) {}

    friend ostream& operator<<(ostream& out, const mint& m) {
        return out << m.x;
    }

    static mint from_unchecked(int x) {
        mint m;
        m.x = x;
        return m;
    }

    mint operator-() const {
        if (!x) {
            return {};
        }
        return mint::from_unchecked(MOD - x);
    }

    mint& operator+=(const mint& m) {
        x += m.x;
        if (x >= MOD) {
            x -= MOD;
        }
        return *this;
    }
    mint& operator-=(const mint& m) {
        return *this += -m;
    }

    mint& operator*=(const mint& m) {
        x = int(long(x) * m.x % MOD);
        return *this;
    }
    mint& operator/=(const mint& m) {
        return *this *= mint::inv(m);
    }

    friend mint operator+(mint a, const mint& b) {
        return a += b;
    }
    friend mint operator-(mint a, const mint& b) {
        return a -= b;
    }
    friend mint operator*(mint a, const mint& b) {
        return a *= b;
    }
    friend mint operator/(mint a, const mint& b) {
        return a /= b;
    }
};

struct Partition {
    static constexpr int MAXN = 17;

    vector<vector<int>> memo[MAXN][MAXN];

    vector<vector<int>> dp(int n, int m) {
        if (!n) {
            return {{}};
        } else if (n < m) {
            return {};
        }

        auto& ans = memo[n][m];

        if (sz(ans)) {
            return ans;
        }

        for (int i = m; i <= n; i++) {
            auto cur = dp(n - i, i);
            for (auto& a : cur) {
                a.insert(a.begin(), i);
            }

            ans.insert(ans.end(), begin(cur), end(cur));
        }

        return ans;
    }

    vector<vector<int>> solve(int n) {
        return dp(n, 1);
    }
} P;

struct M {
    static constexpr int MAXN = 100;

    mint fact[MAXN], ifact[MAXN];

    M() {
        fact[0] = ifact[0] = 1;
        for (int i = 1; i < MAXN; i++) {
            fact[i] = fact[i - 1] * i;
        }
        ifact[MAXN - 1] = mint::inv(fact[MAXN - 1]);
        for (int i = MAXN - 2; i >= 1; i--) {
            ifact[i] = (i + 1) * ifact[i + 1];
        }
    }

    mint choose(int n, int k) const {
        return fact[n] * ifact[k] * ifact[n - k];
    }

    mint choose2(int n, int k) const {
        if (n < 0 || k < 0 || k > n) {
            return 0;
        }
        return choose(n, k);
    }
} M;

namespace s1 {
bool solve(int, int, const vector<pair<int, int>>& edges) {
    if (!sz(edges)) {
        cout << 1 << endl;
        return true;
    }
    return false;
}
}  // namespace s1

namespace s2 {
bool solve(int n, int kv, const vector<pair<int, int>>& edges) {
    if (kv) {
        return false;
    }

    vector<int> graph[n];
    for (auto& [u, v] : edges) {
        graph[u].push_back(v);
    }

    mint dp[1 << n] {};
    dp[(1 << n) - 1] = 1;
    for (int mask = (1 << n) - 2; mask >= 0; mask--) {
        for (int i = 0; i < n; i++) {
            if (on(mask, i)) {
                continue;
            }

            bool bad = false;
            for (auto& v : graph[i]) {
                bad |= on(mask, v);
            }

            if (!bad) {
                dp[mask] += dp[mask | (1 << i)];
            }
        }
    }

    cout << dp[0] / M.fact[n] << endl;

    return true;
}
}  // namespace s2

namespace s3 {

constexpr int MAXN = 20;

vector<int> graph[MAXN];
int vis[MAXN];
bool has_cyc;

void dfs(int u) {
    if (vis[u]) {
        if (vis[u] == 1) {
            has_cyc = true;
        }
        return;
    }

    vis[u] = 1;
    for (auto& v : graph[u]) {
        dfs(v);
    }
    vis[u] = 2;
}

bool solve(int n, int kv, const vector<pair<int, int>>& edges) {
    if (n > 9) {
        return false;
    }

    mint ans = 0;

    for (auto& part : P.solve(n)) {
        int perm[n];
        iota(perm, perm + n, 0);

        do {
            int id[n];
            vector<int> bounds {0};

            for (auto& a : part) {
                int cl = bounds.back(), cr = cl + a;

                for (int i = cl; i < cr; i++) {
                    id[perm[i]] = sz(bounds) - 1;
                }

                bounds.push_back(cr);
            }

            bool bad = false;
            for (int i = 0; i < sz(part) - 1; i++) {
                bad |= part[i] == part[i + 1] &&
                       perm[bounds[i]] > perm[bounds[i + 1]];
            }
            if (bad) {
                continue;
            }

            fill(vis, vis + n, false);
            for (int i = 0; i < n; i++) {
                graph[i].clear();
            }

            has_cyc = false;

            int iperm[n];
            for (int i = 0; i < n; i++) {
                iperm[perm[i]] = i;
            }

            for (auto& [u, v] : edges) {
                if (id[u] == id[v]) {
                    has_cyc |= iperm[u] > iperm[v];
                    continue;
                }
                graph[id[u]].push_back(id[v]);
            }

            for (int i = 0; i < sz(part); i++) {
                dfs(i);
            }

            if (has_cyc) {
                continue;
            }

            int a = sz(part), ck = kv;
            mint cans = M.fact[a];
            ck -= a - 1;
            cans *= M.choose2(ck + a, a);
            ans += cans;
        } while (next_permutation(perm, perm + n));
    }

    cout << ans / (M.fact[n] * M.choose(n + kv, kv)) << endl;

    return true;
}
}  // namespace s3

namespace s4 {

bool solve(int n, int kv, const vector<pair<int, int>>& edges) {
    if (sz(edges) != n * (n - 1) / 2) {
        return false;
    }

    mint ans = 0;

    for (auto& part : P.solve(n)) {
        mint ways = M.fact[sz(part)];
        map<int, int> cnt;
        for (auto& a : part) {
            cnt[a]++;
        }
        for (auto& [_k, v] : cnt) {
            ways /= M.fact[v];
        }

        int a = sz(part), ck = kv;
        mint cans = ways * M.fact[a];
        ck -= a - 1;
        cans *= M.choose2(ck + a, a);
        ans += cans;
    }

    cout << ans / (M.fact[n] * M.choose(n + kv, kv)) << endl;

    return true;
}
}  // namespace s4

namespace s5 {

bool solve(int n, int kv, const vector<pair<int, int>>& edges) {
    if (sz(edges) != n - 1) {
        return false;
    }
    for (auto& [u, v] : edges) {
        if (u) {
            return false;
        }
    }

    mint ans = 0;

    auto get_ways = [&](int a) -> mint {
        int ck = kv;
        mint cans = M.fact[a];
        ck -= a - 1;
        return cans * M.choose2(ck + a, a);
    };

    for (auto& part : P.solve(n - 1)) {
        mint ways = M.fact[n - 1];

        map<int, int> cnt;
        for (auto& a : part) {
            cnt[a]++;
        }
        for (auto& [_k, v] : cnt) {
            ways /= M.fact[v];
        }

        ans += ways * get_ways(sz(part)) * sz(part);
        ans += ways * get_ways(sz(part) + 1);
    }

    cout << ans / (M.fact[n] * M.choose(n + kv, kv)) << endl;

    return true;
}
}  // namespace s5

void solve() {
    int n, m, kv;
    cin >> n >> m >> kv;

    vector<pair<int, int>> edges(m);
    for (auto& [u, v] : edges) {
        cin >> u >> v;
        u--;
        v--;
    }

    bool solved = s1::solve(n, kv, edges) || s2::solve(n, kv, edges) ||
                  s3::solve(n, kv, edges) || s4::solve(n, kv, edges) ||
                  s5::solve(n, kv, edges);
    assert(solved);
}

int main() {
    cin.tie(nullptr);
    cin.exceptions(ios::failbit);
    ios_base::sync_with_stdio(false);
    solve();
}