#include //#include using namespace std; #define lli long long int #define REP(i, s, n) for (lli i = s; i < n; i++) #define INF (1LL << 62) #define mp(a, b) make_pair(a, b) #define SORT(V) sort(V.begin(), V.end()) #define PI (3.141592653589794) #define TO_STRING(VariableName) #VariableName #define LOG1(x) \ if (DEBUG) \ cout << TO_STRING(x) << "=" << x << " " << endl; #define LOG2(x, y) \ if (DEBUG) \ cout << TO_STRING(x) << "=" << x << " " << TO_STRING(y) << "=" << y << endl; #define LOG3(x, y, z) \ if (DEBUG) \ cout << TO_STRING(x) << "=" << x << " " << TO_STRING(y) << "=" << y << " " \ << TO_STRING(z) << "=" << z << endl; #define LOG4(w, x, y, z) \ if (DEBUG) \ cout << TO_STRING(w) << "=" << w << " " << TO_STRING(x) << "=" << x << " " \ << TO_STRING(y) << "=" << y << " " << TO_STRING(z) << "=" << z \ << endl; #define LOG5(w, x, y, z, a) \ if (DEBUG) \ cout << TO_STRING(w) << "=" << w << " " << TO_STRING(x) << "=" << x << " " \ << TO_STRING(y) << "=" << y << " " << TO_STRING(z) << "=" << z << " " \ << TO_STRING(a) << "=" << a << endl; #define LOG6(w, x, y, z, a, b) \ if (DEBUG) \ cout << TO_STRING(w) << "=" << w << " " << TO_STRING(x) << "=" << x << " " \ << TO_STRING(y) << "=" << y << " " << TO_STRING(z) << "=" << z << " " \ << TO_STRING(a) << "=" << a << " " << TO_STRING(b) << "=" << b \ << endl; #define overload6(a, b, c, d, e, f, g, ...) g #define LOG(...) \ overload6(__VA_ARGS__, LOG6, LOG5, LOG4, LOG3, LOG2, LOG1)(__VA_ARGS__) 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; } mt19937 engine; std::chrono::system_clock::time_point start, endTime; #define DEBUG 1 // modint: mod 計算を int を扱うように扱える構造体 template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; } constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; } constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; } constexpr Fp &operator+=(const Fp &r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp &operator-=(const Fp &r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp &operator*=(const Fp &r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp &operator/=(const Fp &r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator==(const Fp &r) const noexcept { return this->val == r.val; } constexpr bool operator!=(const Fp &r) const noexcept { return this->val != r.val; } friend constexpr ostream &operator<<(ostream &os, const Fp &x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; const int MOD = 998244353; using mint = Fp; mint pSum[1000100]; void solve() { // write your code here lli N, M, K; cin >> N >> M >> K; map cnts; REP(i, 0, M) { lli a; cin >> a; cnts[a]++; } REP(i, 0, N + 1) { pSum[i] = 0; } for (auto e : cnts) { auto nowNum = e.first; auto nowCnt = e.second; for (int i = nowNum; i <= N; i += nowNum) { pSum[i] += nowCnt; } } mint ans = 0; REP(i, 1, N + 1) { mint p = pSum[i] / M; mint pp = (mint)1 - p; mint ppp = modpow(pp, K); ans += mint(1) - ppp; } cout << ans << endl; } // Generated by 2.13.0 https://github.com/kyuridenamida/atcoder-tools (tips: // You use the default template now. You can remove this line by using your // custom template) int main() { // Failed to predict input format lli N = 1; // cin >> N; while (N--) solve(); return 0; }