/** * date : 2020-12-01 10:22:56 */ #define NDEBUG #include // #include using namespace std; template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { return pow(mod - 2); } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; using mint = LazyMontgomeryModInt<998244353>; using vm = vector; using vvm = vector; using namespace std; template struct Binomial { vector fac_, finv_, inv_; Binomial(int MAX = 0) : fac_(MAX + 10), finv_(MAX + 10), inv_(MAX + 10) { assert(T::get_mod() != 0); MAX += 9; fac_[0] = finv_[0] = inv_[0] = 1; for (int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i; finv_[MAX] = fac_[MAX].inverse(); for (int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1); for (int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1]; } void extend() { int n = fac_.size(); T fac = fac_.back() * n; T inv = (-inv_[T::get_mod() % n]) * (T::get_mod() / n); T finv = finv_.back() * inv; fac_.push_back(fac); finv_.push_back(finv); inv_.push_back(inv); } T fac(int i) { while (i >= (int)fac_.size()) extend(); return fac_[i]; } T finv(int i) { while (i >= (int)finv_.size()) extend(); return finv_[i]; } T inv(int i) { while (i >= (int)inv_.size()) extend(); return inv_[i]; } T C(int n, int r) { if (n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } T C_naive(int n, int r) { if (n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < r || r < 0) return T(0); return fac(n) * finv(n - r); } T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; Binomial C; using namespace std; // intrinstic // bits // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template void mem(T (&a)[N], int c) { memset(a, c, sizeof(T) * N); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } template int btw(T a, T x, T b) { return a <= x && x < b; } template T ceil(T a, U b) { return (a + b - 1) / b; } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector reord(const vector &v, const vector &ord) { int N = v.size(); vector ret(N); for (int i = 0; i < N; i++) ret[i] = v[ord[i]]; return ret; }; template vector mkiota(int N) { vector ret(N); iota(begin(ret), end(ret), 0); return ret; } template vector mkinv(vector &v, int max_val = -1) { if (max_val < (int)v.size()) max_val = v.size() - 1; vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } __attribute__((target("bmi"))) inline int botbit(const u64 &a) { return _tzcnt_u64(a); } __attribute__((target("bmi"))) inline int ctz(const u64 &a) { return _tzcnt_u64(a); } __attribute__((target("lzcnt"))) inline int topbit(const u64 &a) { return 63 - _lzcnt_u64(a); } __attribute__((target("lzcnt"))) inline int clz64(const u64 &a) { return _lzcnt_u64(a); } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { a ^= (gbit(a, i) == b ? 0 : (T(b) << i)); } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &... u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::type> : true_type {}; template struct is_specialize< U, typename conditional::value>, void>::type> : true_type {}; template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if (is_signed::value) if (t == -Nyaan::inf) res = "-inf"; if (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if (is_signed::value) if (t == -Nyaan::infLL) res = "-inf"; } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? " ]" : ", "); } } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? " ]" : ", "); } } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl using DebugImpl::trace; #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) #endif // macro #define each(x, v) for (auto&& x : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define repc(i, a, cond) for (long long i = (a); (cond); i++) #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define inc(...) \ char __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } using namespace Nyaan; using namespace std; template void walsh_hadamard_transform(vector& f, bool inverse = false) { int n = f.size(); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { T x = f[j], y = f[j | i]; f[j] = x + y, f[j | i] = x - y; } } } if (inverse) { T invn = T(1) / T(f.size()); for (auto& x : f) x *= invn; } } using namespace std; namespace fastio { static constexpr int SZ = 1 << 17; char ibuf[SZ], obuf[SZ]; int pil = 0, pir = 0, por = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } inline void rd(char& c) { c = ibuf[pil++]; } template inline void rd(T& x) { if (pil + 32 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if (c == '-') { minus = 1; c = ibuf[pil++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = ibuf[pil++]; } if (minus) x = -x; } inline void rd() {} template inline void rd(Head& head, Tail&... tail) { rd(head); rd(tail...); } inline void wt(char c) { obuf[por++] = c; } template inline void wt(T x) { if (por > SZ - 32) flush(); if (!x) { obuf[por++] = '0'; return; } if (x < 0) { obuf[por++] = '-'; x = -x; } int i = 12; char buf[16]; while (x >= 10000) { memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; i -= 4; } if (x < 100) { if (x < 10) { wt(char('0' + char(x))); } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; obuf[por + 0] = '0' + q; obuf[por + 1] = '0' + r; por += 2; } } else { if (x < 1000) { memcpy(obuf + por, pre.num + (x << 2) + 1, 3); por += 3; } else { memcpy(obuf + por, pre.num + (x << 2), 4); por += 4; } } memcpy(obuf + por, buf + i + 4, 12 - i); por += 12 - i; } inline void wt() {} template inline void wt(Head head, Tail... tail) { wt(head); wt(tail...); } template inline void wtn(T x) { wt(x, '\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::wt; using fastio::wtn; void Nyaan::solve() { int n, k, x, y; rd(n, k, x, y); vi a(k); each(i, a) rd(i); a = mkuni(a); V dp(sz(a), vm(1024)); auto dfs = [&](auto rc, int i, int v, int par) -> void { if (i == n / 2) { dp[lb(a, par)][v] += 1; } else { each(j, a) if (j != par) rc(rc, i + 1, v ^ j, j); } }; dfs(dfs, 0, 0, -1); mint ans = 0; vm sm(1024); rep(i, sz(a)) rep(j, 1024) sm[j] += dp[i][j]; walsh_hadamard_transform(sm); each(x_, sm) x_ *= x_; walsh_hadamard_transform(sm); each(x_, sm) x_ *= mint(1024).inverse(); rep(i, 1024) if (x <= i and i <= y) ans += sm[i]; rep(i, sz(a)) { walsh_hadamard_transform(dp[i]); each(x_, dp[i]) x_ *= x_; walsh_hadamard_transform(dp[i]); each(x_, dp[i]) x_ *= mint(1024).inverse(); rep(j, 1024) if (x <= j and j <= y) ans -= dp[i][j]; } wtn(ans.get()); }