#pragma GCC target ("avx") #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #define _USE_MATH_DEFINES #include<iostream> #include<string> #include<queue> #include<cmath> #include<map> #include<set> #include<list> #include<iomanip> #include<vector> #include<random> #include<functional> #include<algorithm> #include<stack> #include<cstdio> #include<cstring> #include<bitset> #include<unordered_map> #include<climits> #include<fstream> #include<complex> #include<time.h> #include<cassert> #include<functional> #include<numeric> #include<tuple> using namespace std; using ll = long long; using ld = long double; #define int long long #define all(a) (a).begin(),(a).end() #define fs first #define sc second #define xx first #define yy second.first #define zz second.second #define H pair<int, int> #define P pair<int, pair<int, int>> #define Q(i,j,k) mkp(i,mkp(j,k)) #define rng(i,s,n) for(int i = (s) ; i < (n) ; i++) #define rep(i,n) rng(i, 0, (n)) #define mkp make_pair #define vec vector #define vi vec<int> #define pb emplace_back #define siz(a) (int)(a).size() #define crdcomp(b) sort(all((b)));(b).erase(unique(all((b))),(b).end()) #define getidx(b,i) lower_bound(all(b),(i))-(b).begin() #define ssp(i,n) (i==(int)(n)-1?"\n":" ") #define ctoi(c) (int)(c-'0') #define itoc(c) (char)(c+'0') #define cyes printf("Yes\n") #define cno printf("No\n") #define cdf(n) int quetimes_=(n);rep(qq123_,quetimes_) #define gcj printf("Case #%lld: ",qq123_+1) #define readv(a,n) a.resize(n,0);rep(i,(n)) a[i]=read() #define found(a,x) (a.find(x)!=a.end()) //#define endl "\n" constexpr int mod = 1e9 + 7; constexpr int Mod = 998244353; constexpr ld EPS = 1e-10; constexpr ll inf = 3 * 1e18; constexpr int Inf = 15 * 1e8; constexpr int dx[] = { -1,1,0,0 }, dy[] = { 0,0,-1,1 }; template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } ll read() { ll u, k = scanf("%lld", &u); return u; } string reads() { string s; cin >> s; return s; } H readh(bool g = 0) { H u; int k = scanf("%lld %lld", &u.fs, &u.sc); if (g) u.fs--, u.sc--; return u; } bool ina(H t, int h, int w) { return 0 <= t.fs && t.fs < h && 0 <= t.sc && t.sc < w; } bool ina(int t, int l, int r) { return l <= t && t < r; } ll gcd(ll i, ll j) { return j ? gcd(j, i % j) : i; } ll popcount(ll x) { int sum = 0; for (int i = 0; i < 60; i++)if ((1ll << i) & x) sum++; return sum; } class mint { public:ll v; mint(ll v = 0) { s(v % mod + mod); } constexpr static int mod = 1e9 + 7; constexpr static int fn_ = 3e5 + 5; static mint fact[fn_], comp[fn_]; mint pow(int x) const { mint b(v), c(1); while (x) { if (x & 1) c *= b; b *= b; x >>= 1; } return c; } inline mint& s(int vv) { v = vv < mod ? vv : vv - mod; return *this; } inline mint inv()const { return pow(mod - 2); } inline mint operator-()const { return mint() - *this; } inline mint& operator+=(const mint b) { return s(v + b.v); } inline mint& operator-=(const mint b) { return s(v + mod - b.v); } inline mint& operator*=(const mint b) { v = v * b.v % mod; return *this; } inline mint& operator/=(const mint b) { v = v * b.inv().v % mod; return *this; } inline mint operator+(const mint b) const { return mint(v) += b; } inline mint operator-(const mint b) const { return mint(v) -= b; } inline mint operator*(const mint b) const { return mint(v) *= b; } inline mint operator/(const mint b) const { return mint(v) /= b; } friend ostream& operator<<(ostream& os, const mint& m) { return os << m.v; } friend istream& operator>>(istream& is, mint& m) { int x; is >> x; m = mint(x); return is; } bool operator<(const mint& r)const { return v < r.v; } bool operator>(const mint& r)const { return v > r.v; } bool operator<=(const mint& r)const { return v <= r.v; } bool operator>=(const mint& r)const { return v >= r.v; } bool operator==(const mint& r)const { return v == r.v; } bool operator!=(const mint& r)const { return v != r.v; } explicit operator bool()const { return v; } explicit operator int()const { return v; } mint comb(mint k) { if (k > * this) return mint(); if (!fact[0]) combinit(); if (v >= fn_) { if (k > * this - k) k = *this - k; mint tmp(1); for (int i = v; i >= v - k.v + 1; i--) tmp *= mint(i); return tmp * comp[k.v]; } return fact[v] * comp[k.v] * comp[v - k.v]; }//nCk mint perm(mint k) { if (k > * this) return mint(); if (!fact[0]) combinit(); if (v >= fn_) { mint tmp(1); for (int i = v; i >= v - k.v + 1; i--) tmp *= mint(i); return tmp; } return fact[v] * comp[v - k.v]; } static void combinit() { fact[0] = 1; for (int i = 1; i < fn_; i++) fact[i] = fact[i - 1] * mint(i); comp[fn_ - 1] = fact[fn_ - 1].inv(); for (int i = fn_ - 2; i >= 0; i--) comp[i] = comp[i + 1] * mint(i + 1); } }; mint mint::fact[fn_], mint::comp[fn_]; //-------------------------------------------------------------- class Matrix { public: int h, w; int dat[300][300]; static Matrix c, d; void init(int height, int width) { h = height, w = width; for (int i = 0; i < h; i++)for (int j = 0; j < w; j++) dat[i][j] = 0; } auto operator[](int i) { return dat[i]; } void operator+=(Matrix& b) { for (int i = 0; i < h; i++)for (int j = 0; j < w; j++) dat[i][j] += b.dat[i][j]; } void operator-=(Matrix& b) { for (int i = 0; i < h; i++)for (int j = 0; j < w; j++) dat[i][j] -= b.dat[i][j]; } Matrix operator+(Matrix& b) { c = *this; c += b; return c; } Matrix operator-(Matrix& b) { c = *this; c -= b; return c; } Matrix operator*(Matrix& b) { c.init(h, b.w); for (int i = 0; i < h; i++)for (int j = 0; j < w; j++)for (int k = 0; k < b.w; k++) { c.dat[i][k] += dat[i][j] * b.dat[j][k]; } return c; } void operator%=(int& b) { for (int i = 0; i < h; i++)for (int j = 0; j < w; j++) dat[i][j] %= b; } Matrix operator%(int& b) { c = *this; c %= b; return c; } void operator*=(int& b) { for (int i = 0; i < h; i++)for (int j = 0; j < w; j++) dat[i][j] *= b; } Matrix operator*(int& b) { c = *this; c *= b; return c; } Matrix moddot(Matrix& a, Matrix& b, int Mod = mod) { c.init(a.h, b.w); for (int i = 0; i < a.h; i++)for (int j = 0; j < a.w; j++)for (int k = 0; k < b.w; k++) { (c.dat[i][k] += a.dat[i][j] * b.dat[j][k] % Mod) %= Mod; } return c; } Matrix mod_pow(int k, int Mod = mod) { c.init(h, w); d = *this; for (int i = 0; i < h; i++) c[i][i] = 1; while (k) { if (k & 1) { c = moddot(c, d); c %= Mod; } d = moddot(d, d); d %= Mod; k >>= 1; } return c; } }; Matrix Matrix::c, Matrix::d; //--------------------------------------------------------------------- int k, m, n; vec<P>a; Matrix mat; signed main() { cin >> k >> m >> n; rep(i, m) { int u, v, r; cin >> u >> v >> r; a.pb(Q(u, v, r)); } //どうせ行列累乗 //i,i-1音のところで何通りあるか? //a[6][2] mat.init(m, m); rep(i, m)rep(j, m) { if (a[i].yy == a[j].xx && a[i].zz == a[j].yy) { mat[i][j] = 1; } } mat = mat.mod_pow(n - 2, mod); mint sum = 0; rep(i, m)rep(j, m) sum += mat[i][j]; cout << sum << endl; }