#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const tuple& t) { os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')'; return os; } template ostream& operator<<(ostream& os, const tuple& t) { os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion /** * @brief modint * @docs docs/modulo/modint.md */ template class modint { using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; public: u32 v; constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {} constexpr u32& value() noexcept { return v; } constexpr const u32& value() const noexcept { return v; } constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint& operator+=(const modint& rhs) noexcept { v += rhs.v; if (v >= mod) v -= mod; return *this; } constexpr modint& operator-=(const modint& rhs) noexcept { if (v < rhs.v) v += mod; v -= rhs.v; return *this; } constexpr modint& operator*=(const modint& rhs) noexcept { v = (u64)v * rhs.v % mod; return *this; } constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); } constexpr modint pow(u64 exp) const noexcept { modint self(*this), res(1); while (exp > 0) { if (exp & 1) res *= self; self *= self; exp >>= 1; } return res; } constexpr modint& operator++() noexcept { if (++v == mod) v = 0; return *this; } constexpr modint& operator--() noexcept { if (v == 0) v = mod; return --v, *this; } constexpr modint operator++(int) noexcept { modint t = *this; return ++*this, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --*this, t; } constexpr modint operator-() const noexcept { return modint(mod - v); } template friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; } template friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; } template friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; } template friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; } constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; } constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; } constexpr bool operator!() const noexcept { return !v; } friend istream& operator>>(istream& s, modint& rhs) noexcept { i64 v; rhs = modint{(s >> v, v)}; return s; } friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; } }; const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; using mint = modint; int main() { cin.tie(0); ios::sync_with_stdio(false); int N, M, K; cin >> N >> M >> K; K--; vector>> G(N); for (; M--;) { int X, Y, Z; cin >> X >> Y >> Z; X--, Y--, Z -= 2; if (Z < 0) { cout << 0 << '\n'; return 0; } G[X].emplace_back(Y, Z); G[Y].emplace_back(X, Z); } vector dep(N, -1); vector val(N); vector visited; bool ok = true; ll det = -1; auto dfs = [&](auto self, int v, int d, ll x) -> void { dep[v] = d; val[v] = x; visited.emplace_back(v); for (auto& e : G[v]) { int u = e.first; if (~dep[u]) { if (dep[v] != dep[u]) { if (val[v] + val[u] != e.second) { ok = false; } } else { ll sum = -val[v] - val[u] + e.second; if (dep[v]) sum *= -1; if (sum < 0 || (sum & 1LL)) ok = false; if (det < 0) det = sum / 2; else if (det != sum / 2) ok = false; } continue; } self(self, u, d ^ 1, e.second - x); } }; auto calc = [&](int k) -> mint { // \forall i, A_i \leq k if (k < 0) return 0; mint res = 1; for (int i = 0; i < N; i++) { if (~dep[i]) continue; dfs(dfs, i, 0, 0); if (!ok) res = 0; if (det > k) res = 0; ll Max = k, Min = 0; for (int& v : visited) { if (det >= 0) { Min = det; Max = det; ll z = val[v] + (dep[v] ? -det : det); if (z < 0 || k < z) res = 0; } else { if (dep[v]) { chmin(Max, val[v]); chmax(Min, val[v] - k); } else { chmax(Min, -val[v]); chmin(Max, k - val[v]); } } } res *= max(0LL, Max - Min + 1); // debug(i, Min, Max, res, visited, ok, val); visited.clear(); ok = true; det = -1; } for (int i = 0; i < N; i++) dep[i] = -1; // debug(k, res); return res; }; cout << calc(K) - calc(K - 1) << '\n'; return 0; }