#include #include #include #include #include #include #include #include #define _fetch(_1, _2, _3, _4, name, ...) name #define rep2(i, n) rep3(i, 0, n) #define rep3(i, a, b) rep4(i, a, b, 1) #define rep4(i, a, b, c) for (int i = int(a); i < int(b); i += int(c)) #define rep(...) _fetch(__VA_ARGS__, rep4, rep3, rep2, _)(__VA_ARGS__) using namespace std; using i64 = long long; using u32 = unsigned; using u64 = unsigned long long; using f80 = long double; namespace ntt { template class Mod64 { private: using u128 = __uint128_t; static constexpr u64 mul_inv(u64 n, int e=6, u64 x=1) { return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n)); } public: static constexpr u64 inv = mul_inv(mod); static constexpr u64 r2 = -u128(mod) % mod; static constexpr int level = __builtin_ctzll(mod - 1); static_assert(inv * mod == 1, "invalid 1/M modulo 2^64."); Mod64() {} Mod64(u64 n) : x(init(n)) {}; static u64 modulo() { return mod; } static u64 init(u64 w) { return reduce(u128(w) * r2); } static u64 reduce(const u128 w) { return u64(w >> 64) + mod - ((u128(u64(w) * inv) * mod) >> 64); } static Mod64 omega() { return Mod64(prim_root).pow((mod - 1) >> level); } Mod64& operator += (Mod64 rhs) { this->x += rhs.x; return *this; } Mod64& operator -= (Mod64 rhs) { this->x += 2 * mod - rhs.x; return *this; } Mod64& operator *= (Mod64 rhs) { this->x = reduce(u128(this->x) * rhs.x); return *this; } Mod64 operator + (Mod64 rhs) const { return Mod64(*this) += rhs; } Mod64 operator - (Mod64 rhs) const { return Mod64(*this) -= rhs; } Mod64 operator * (Mod64 rhs) const { return Mod64(*this) *= rhs; } u64 get() const { return reduce(this->x) % mod; } void set(u64 n) const { this->x = n; } Mod64 pow(u64 exp) const { Mod64 ret = Mod64(1); for (Mod64 base = *this; exp; exp >>= 1, base *= base) if (exp & 1) ret *= base; return ret; } Mod64 inverse() const { return pow(mod - 2); } friend ostream& operator << (ostream& os, const Mod64& m) { return os << m.get(); } static void debug() { printf("%llu %llu %llu %llu\n", mod, inv, r2, omega().get()); } u64 x; }; template void convolute(mod_t* A, int s1, mod_t* B, int s2) { int s = s1 + s2 - 1; int size = 1; while (size < s) size <<= 1; mod_t roots[mod_t::level] = { mod_t::omega() }; rep(i, 1, mod_t::level) roots[i] = roots[i - 1] * roots[i - 1]; fill(A + s1, A + size, 0); ntt_dit4(A, size, 1, roots); if (A == B && s1 == s2) { rep(i, size) A[i] *= A[i]; } else { fill(B + s2, B + size, 0); ntt_dit4(B, size, 1, roots); rep(i, size) A[i] *= B[i]; } ntt_dit4(A, size, -1, roots); mod_t inv = mod_t(size).inverse(); rep(i, s) A[i] *= inv; } template void rev_permute(mod_t* A, int n) { int r = 0, nh = n >> 1; rep(i, 1, n) { for (int h = nh; !((r ^= h) & h); h >>= 1); if (r > i) swap(A[i], A[r]); } } template void ntt_dit4(mod_t* A, int n, int sign, mod_t* roots) { rev_permute(A, n); int logn = __builtin_ctz(n); if (logn & 1) rep(i, 0, n, 2) { mod_t a = A[i], b = A[i + 1]; A[i] = a + b; A[i + 1] = a - b; } mod_t imag = roots[mod_t::level - 2]; if (sign < 0) imag = imag.inverse(); mod_t one = mod_t(1); rep(e, 2 + (logn & 1), logn + 1, 2) { const int m = 1 << e; const int m4 = m >> 2; mod_t dw = roots[mod_t::level - e]; if (sign < 0) dw = dw.inverse(); const int block_size = max(m, (1 << 15) / int(sizeof(A[0]))); rep(k, 0, n, block_size) { mod_t w = one, w2 = one, w3 = one; rep(j, m4) { rep(i, k + j, k + block_size, m) { mod_t a0 = A[i + m4 * 0] * one, a2 = A[i + m4 * 1] * w2; mod_t a1 = A[i + m4 * 2] * w, a3 = A[i + m4 * 3] * w3; mod_t t02 = a0 + a2, t13 = a1 + a3; A[i + m4 * 0] = t02 + t13; A[i + m4 * 2] = t02 - t13; t02 = a0 - a2, t13 = (a1 - a3) * imag; A[i + m4 * 1] = t02 + t13; A[i + m4 * 3] = t02 - t13; } w *= dw; w2 = w * w; w3 = w2 * w; } } } } const int size = 1 << 17; using m64 = ntt::Mod64<31525197391593473, 3>; m64 f[size], g[size]; } // namespace ntt #define getchar getchar_unlocked #define putchar putchar_unlocked int get_int() { int n; char c; while ((c = getchar()) < '0'); n = c - '0'; while ((c = getchar()) >= '0') n = n * 10 + c - '0'; return n; } void put_u32(u32 n) { char strs[11]; int i = 0; do { strs[i++] = n % 10, n /= 10; } while (n); while (i) putchar('0' + strs[--i]); putchar('\n'); } int main() { using namespace ntt; int L = get_int(), M = get_int(), N = get_int(); const u32 s = 17, mask = 1 << s; auto one = m64(1), one17 = m64(mask); rep(i, L) { int n = get_int(); f[n >> 1] += (n & 1) ? one17 : one; } rep(i, M) { int n = N - get_int(); g[n >> 1] += (n & 1) ? one17 : one; } ntt::convolute(f, N / 2 + 1, g, N / 2 + 1); int Q = get_int(); static int res[200010]; u64 carry = 0; rep(i, 0, (N + Q + 1) / 2) { u64 n = f[i].get() + carry; res[2 * i + 0] = n & (mask - 1); res[2 * i + 1] = (n >> s) & (mask - 1); carry = n >> (2 * s); } rep(i, N, N + Q) put_u32(res[i]); return 0; }