#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))

struct IO {
    char buf[40 << 20], *i = buf;

    IO() {
        std::ignore = fread_unlocked(buf, 1, sizeof(buf), stdin);
    }

    template <typename T>
    IO& operator>>(T& x) {
        while (*i < '0') {
            i++;
        }

        x = 0;

        while (*i >= '0') {
            x = x * 10 + (*(i++) ^ '0');
        }

        return *this;
    }
} io;

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 << "]";
}

template <typename A, typename B>
ostream& operator<<(ostream& out, const pair<A, B>& p) {
    return out << "(" << p.first << ", " << p.second << ")";
}

constexpr int MAXN = 2e3 + 5;

struct Dim {
    int id, len, ret;

    friend bool operator==(const Dim& lhs, const Dim& rhs) {
        return std::tie(lhs.id, lhs.len, lhs.ret) ==
               std::tie(rhs.id, rhs.len, rhs.ret);
    }
    friend bool operator!=(const Dim& lhs, const Dim& rhs) {
        return !(lhs == rhs);
    }

    friend bool operator<(const Dim& lhs, const Dim& rhs) {
        return std::tie(lhs.id, lhs.len, lhs.ret) <
               std::tie(rhs.id, rhs.len, rhs.ret);
    }
    friend bool operator<=(const Dim& lhs, const Dim& rhs) {
        return !(rhs < lhs);
    }
    friend bool operator>(const Dim& lhs, const Dim& rhs) {
        return rhs < lhs;
    }
    friend bool operator>=(const Dim& lhs, const Dim& rhs) {
        return !(lhs < rhs);
    }
};

constexpr int MOD = 998244353;

struct mint {
    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() {}
    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 M {
    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[i] = mint::inv(fact[i]);
        }
    }

    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 || n < k || k < 0) {
            return 0;
        }
        return choose(n, k);
    }
} M;

struct Factor {
    vector<int> facts[MAXN];

    Factor() {
        for (int i = 1; i < MAXN; i++) {
            for (int j = i; j < MAXN; j += i) {
                facts[j].push_back(i);
            }
        }
    }
} F;

namespace p2 {

using mat = vector<vector<mint>>;

mat operator*(const mat& a, const mat& b) {
    int n1 = sz(a), n2 = sz(b), n3 = sz(b[0]);

    mat ans(n1, vector<mint>(n3));

    for (int i = 0; i < n1; i++) {
        for (int j = 0; j < n2; j++) {
            for (int k = 0; k < n3; k++) {
                ans[i][k] += a[i][j] * b[j][k];
            }
        }
    }

    return ans;
}

mat bpow(mat base, long exp) {
    mat ans;

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

    return ans;
}

// put a things into b groups
mint solve_group(int a, int b) {
    assert(a % b == 0);
    return M.fact[a] / mint::pow(a / b, b) * M.ifact[b];
}

mint solve2(int x, int m, long kv) {
    auto& m_fact = F.facts[m];

    int n = sz(m_fact);

    mat cmat(n, vector<mint>(n));

    for (int c1 = 0; c1 < n; c1++) {
        for (int c2 = c1; c2 < n; c2++) {
            int i = m_fact[c1], j = m_fact[c2];

            if (j % i) {
                continue;
            }

            mint cbase = mint(i) * x;
            int u = j / i;
            cmat[c1][c2] = mint::pow(cbase, 1 + (u - 1) * m / j) *
                           solve_group(m / i, m / j);
        }
    }

    return bpow(cmat, kv)[0].back();
    // mint dp[kv + 1][m + 1] {};
    // dp[kv][m] = 1;
    //
    // for (int kit = kv - 1; kit >= 0; kit--) {
    //     for (auto& i : m_fact) {
    //         mint cbase = mint(i) * x;
    //
    //         for (int j = i; j <= m; j += i) {
    //             if (m % j) {
    //                 continue;
    //             }
    //
    //             int u = j / i;
    //             dp[kit][i] += dp[kit + 1][j] *
    //                           mint::pow(cbase, 1 + (u - 1) * m / j) *
    //                           solve_group(m / i, m / j);
    //         }
    //
    //         // dp[kit][i] *= mint::pow(mint(i) * x, m / i);
    //         dbg(kit, i, dp[kit][i]);
    //     }
    // }
    //
    // return dp[0][1];
}

mint solve(int x, int w, long kv) {
    mint trans[w + 1];
    for (int m = 1; m <= w; m++) {
        trans[m] = solve2(x, m, kv);
        dbg(x, m, trans[m]);
    }

    mint dp[w + 1] {};
    dp[0] = 1;

    for (int i = 1; i <= w; i++) {
        for (int j = 1; j <= i; j++) {
            dp[i] += trans[j] * dp[i - j] * M.choose(i - 1, j - 1);
        }
    }

    return dp[w];
}

void solve(const vector<pair<int, int>>& arr, long kv) {
    mint ans = 1;

    for (auto& [x, w] : arr) {
        ans *= solve(x, w, kv);
    }

    cout << ans << endl;
}

}  // namespace p2

int arr[MAXN][MAXN], par[MAXN], label[MAXN];
vector<Dim> comps[MAXN], comps_full[MAXN];

template <typename Cb>
void relabel(int u, const vector<Dim>& dims, int ind, int cur, const Cb& cb) {
    if (ind == sz(dims)) {
        label[u] = cur;
        cb(u);
        return;
    }

    auto& cd = dims[ind];
    cur *= cd.len;
    for (int i = 0; i < cd.len; i++) {
        relabel(u, dims, ind + 1, cur, cb);
        cur++;
        u = arr[cd.id][u];
    }
}

void solve() {
    // cout << p2::solve2(1, 4, 2) << endl;
    // return;
    int tc_id, n, m;
    long kv;
    io >> tc_id >> n >> m >> kv;

    for (int i = 0; i < n * m; i++) {
        int u, v, w;
        io >> u >> v >> w;
        u--;
        v--;
        w--;
        arr[w][u] = v;
    }

    iota(par, par + n, 0);

    for (int p_id = 0; p_id < m; p_id++) {
        for (int u = 0; u < n; u++) {
            if (par[u] != u) {
                continue;
            }

            int cu = u, len = 0;
            while (true) {
                assert(comps[u] == comps[par[cu]]);
                cu = arr[p_id][cu];
                len++;
                if (par[cu] == u) {
                    break;
                }
            }

            if (len == 1) {
                comps_full[u].push_back({p_id, len, label[cu]});
                continue;
            }

            comps[u].push_back({p_id, len, -1});

            relabel(u, comps[u], 0, 0, [&](int v) -> void {
                par[v] = u;
            });

            comps[u].back().ret = label[cu];
            comps_full[u].push_back({p_id, len, label[cu]});
        }
    }

    int sizes[n] {};
    for (int i = 0; i < n; i++) {
        sizes[par[i]]++;
    }

    map<vector<Dim>, pair<int, int>> comp_occ;
    for (int i = 0; i < n; i++) {
        if (par[i] != i) {
            continue;
        }

        auto [it, inserted] = comp_occ.insert({comps_full[i], {sizes[i], 1}});
        if (!inserted) {
            auto& [szs, cnt] = it->second;
            assert(szs == sizes[i]);
            cnt++;
        }
    }

    vector<pair<int, int>> narr;
    for (auto& [_k, v] : comp_occ) {
        narr.push_back(v);
    }

    dbg(narr, kv);
    p2::solve(narr, kv);
}

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