#include "bits/stdc++.h" #include #include #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define SZ(x) ((lint)(x).size()) #define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i=i##_begin_;--i) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) #define endk '\n' using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef long double ld; typedef pair plint; typedef pair pld; struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; template auto add = [](T a, T b) -> T { return a + b; }; template auto mul = [](T a, T b) -> T { return a * b; }; template auto f_max = [](T a, T b) -> T { return max(a, b); }; template auto f_min = [](T a, T b) -> T { return min(a, b); }; template using V = vector; using Vl = V; using VVl = V; template< typename T > ostream& operator<<(ostream& os, const vector< T >& v) { for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != v.size() ? " " : ""); return os; } template< typename T >istream& operator>>(istream& is, vector< T >& v) { for (T& in : v) is >> in; return is; } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } template T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } template struct rec { F f; rec(F&& f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); } lint digit(lint a) { return (lint)log10(a); } lint e_dist(plint a, plint b) { return abs(a.first - b.first) * abs(a.first - b.first) + abs(a.second - b.second) * abs(a.second - b.second); } lint m_dist(plint a, plint b) { return abs(a.first - b.first) + abs(a.second - b.second); } bool check_overflow(lint a, lint b, lint limit) { if (b == 0) return false; return a > limit / b; } // a * b > c => true void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); } const lint MOD1000000007 = 1000000007, MOD998244353 = 998244353, INF = 2e9; lint dx[8] = { 0, -1, 0, 1, 1, -1, 1, -1 }, dy[8] = { -1, 0, 1, 0, -1, -1, 1, 1 }; bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; } struct Edge { lint from, to; lint cost; Edge() { } Edge(lint u, lint v, lint c) { cost = c; from = u; to = v; } bool operator<(const Edge& e) const { return cost < e.cost; } }; struct WeightedEdge { lint to; lint cost; WeightedEdge(lint v, lint c = 1) { to = v; cost = c; } bool operator<(const WeightedEdge& e) const { return cost < e.cost; } }; using WeightedGraph = V>; typedef pair tlint; typedef pair qlint; typedef pair valstr; typedef pair valv; template struct Matrix_Powers { public: V> Matrix; V dp; int sz; Matrix_Powers(int _sz) : Matrix(_sz, V(_sz, 0)), dp(_sz, 0), sz(_sz) { }; void Matrix_Pow(lint k) { while (k) { if (k & 1) Matrix_Mul(); Update(); k /= 2; } } private: void Matrix_Mul() { V res(sz); REP(i, sz) REP(j, sz) res[i] += Matrix[i][j] * dp[j]; dp = res; } void Update() { V> res(sz, V(sz)); REP(i, sz) { REP(j, sz) { REP(k, sz) { res[i][j] += Matrix[i][k] * Matrix[k][j]; } } } Matrix = res; } }; \ template class modint { using u64 = std::int_fast64_t; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(x% Modulus) {} constexpr u64& value() noexcept { return a; } constexpr const u64& value() const noexcept { return a; } 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 { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint& operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint& operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint& operator/=(modint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } }; typedef modint ModInt; ModInt mod_pow(ModInt x, lint n) { ModInt ret = 1; while (n > 0) { if (n & 1) (ret *= x); (x *= x); n >>= 1; } return ret; } ModInt func[200000]; void funcinit(int N) { func[0] = 1; for (int i = 1; i <= N; i++) { func[i] = func[i - 1] * i; } } ModInt comb(ModInt n, ModInt r) { if (n.a <= 0 || n.a < r.a) { return 1; } return func[n.a] / (func[r.a] * func[(n - r).a]); } int main() { lint N, M, T; cin >> N >> M >> T; Matrix_Powers mat(N); REP(i, M) { lint u, v; cin >> u >> v; mat.Matrix[u][v] = 1; mat.Matrix[v][u] = 1; } mat.dp[0] = 1; mat.Matrix_Pow(T); cout << mat.dp[0].a << endk; }