#ifndef LOCAL #define FAST_IO #endif // ============ #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i) #define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i) #define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__) #define ALL(x) begin(x), end(x) #define LEN(x) (i32)(x.size()) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; using pi = pair; using pl = pair; template using V = vector; template using VV = V>; template using VVV = V>>; template using VVVV = V>>>; template using PQR = priority_queue, greater>; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } template i32 lob(const V &arr, const T &v) { return (i32)(lower_bound(ALL(arr), v) - arr.begin()); } template i32 upb(const V &arr, const T &v) { return (i32)(upper_bound(ALL(arr), v) - arr.begin()); } template V argsort(const V &arr) { V ret(arr.size()); iota(ALL(ret), 0); sort(ALL(ret), [&](i32 i, i32 j) -> bool { if (arr[i] == arr[j]) { return i < j; } else { return arr[i] < arr[j]; } }); return ret; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; void scan(char &x) { cin >> x; } void scan(u32 &x) { cin >> x; } void scan(u64 &x) { cin >> x; } void scan(i32 &x) { cin >> x; } void scan(i64 &x) { cin >> x; } void scan(string &x) { cin >> x; } template void scan(V &x) { for (T &ele : x) { scan(ele); } } void read() {} template void read(Head &head, Tail &...tail) { scan(head); read(tail...); } #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__); #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__); #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__); #define I32(...) \ i32 __VA_ARGS__; \ read(__VA_ARGS__); #define I64(...) \ i64 __VA_ARGS__; \ read(__VA_ARGS__); #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__); #define VEC(type, name, size) \ V name(size); \ read(name); #define VVEC(type, name, size1, size2) \ VV name(size1, V(size2)); \ read(name); // ============ #ifdef DEBUGF #else #define DBG(...) (void)0 #endif // ============ // ============ // ============ #include #include #include namespace poly { using Mint = atcoder::modint998244353; using Poly = std::vector; Poly add(Poly f, Poly g) { if (f.size() < g.size()) { std::swap(f, g); } for (int i = 0; i < (int)g.size(); ++i) { f[i] += g[i]; } return f; } Poly sub(Poly f, Poly g) { if (f.size() < g.size()) { std::swap(f, g); } for (int i = 0; i < (int)g.size(); ++i) { f[i] -= g[i]; } return f; } Poly mul(const Poly &f, const Poly &g) { return atcoder::convolution(f, g); } void dft(Poly &f) { atcoder::internal::butterfly(f); } void idft(Poly &f) { atcoder::internal::butterfly_inv(f); int ctz = __builtin_ctz((int)f.size()); Mint inv = Mint::raw(Mint::mod() - (Mint::mod() >> ctz)); for (Mint &cf : f) { cf *= inv; } } } // namespace poly // ============ namespace poly { class Factorial { std::vector fac; std::vector ifac; public: Factorial() : fac(1, Mint::raw(1)), ifac(1, Mint::raw(1)) {} void reserve(int n) { int m = (int)fac.size() - 1; if (n <= m) { return; } fac.resize(n + 1); for (int i = m + 1; i <= n; ++i) { fac[i] = fac[i - 1] * Mint::raw(i); } ifac.resize(n + 1); ifac[n] = fac[n].inv(); for (int i = n - 1; i >= m; --i) { ifac[i] = ifac[i + 1] * Mint::raw(i + 1); } } Mint fact(int n) const { assert(n < (int)fac.size()); return fac[n]; } Mint inv_fact(int n) const { assert(n < (int)fac.size()); return ifac[n]; } Mint inv_n(int n) const { assert(n < (int)fac.size()); return ifac[n] * fac[n - 1]; } Mint binom(int n, int r) const { assert(n < (int)fac.size()); return fac[n] * ifac[r] * ifac[n - r]; } } factorial; } // namespace poly // ============ namespace poly { Poly taylor_shift(Poly f, Mint c) { int n = (int)f.size(); factorial.reserve(n); for (int i = 0; i < n; ++i) { f[i] *= factorial.fact(i); } std::reverse(f.begin(), f.end()); Mint pw(1); Poly g(n); for (int i = 0; i < n; ++i) { g[i] = pw * factorial.inv_fact(i); pw *= c; } Poly h = mul(f, g); h.resize(n); std::reverse(h.begin(), h.end()); for (int i = 0; i < n; ++i) { h[i] *= factorial.inv_fact(i); } return h; } } // namespace poly // ============ void solve() { using M = poly::Mint; I32(n, k); VEC(i32, a, n); poly::factorial.reserve(n); sort(ALL(a)); reverse(ALL(a)); poly::Poly f(n); REP(i, n) { f[i] = M::raw(a[i]); } poly::Poly g = poly::taylor_shift(f, M(1)); g.insert(g.begin(), M()); DBG(g); REP(i, n + 1) { g[i] /= poly::factorial.binom(n, i); } M exp; REP(i, n - 1) { i32 len = min(i + 1, k) + min(n - 1 - i, k); exp += g[len]; } exp *= poly::factorial.fact(n); cout << exp.val() << '\n'; } int main() { i32 t = 1; // cin >> t; while (t--) { solve(); } }