#include #include #include #include #include #include #include #include #define _rep(_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(...) _rep(__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 { using word_t = u64; using dword_t = __uint128_t; static constexpr word_t mul_inv(word_t n, int e=6, word_t x=1) { return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n)); } template class UnsafeMod { private: static const int word_bits = 8 * sizeof(word_t); public: static constexpr word_t inv = mul_inv(mod); static constexpr word_t r2 = -dword_t(mod) % mod; static constexpr int level = __builtin_ctzll(mod - 1); static_assert(inv * mod == 1, "invalid 1/M modulo 2^@."); UnsafeMod() {} UnsafeMod(word_t n) : x(init(n)) {}; static word_t modulus() { return mod; } static word_t init(word_t w) { return reduce(dword_t(w) * r2); } static word_t reduce(const dword_t w) { return word_t(w >> word_bits) + mod - word_t((dword_t(word_t(w) * inv) * mod) >> word_bits); } static UnsafeMod omega() { return UnsafeMod(prim_root).pow((mod - 1) >> level); } UnsafeMod& operator += (UnsafeMod rhs) { x += rhs.x; return *this; } UnsafeMod& operator -= (UnsafeMod rhs) { x += 3 * mod - rhs.x; return *this; } UnsafeMod& operator *= (UnsafeMod rhs) { x = reduce(dword_t(x) * rhs.x); return *this; } UnsafeMod operator + (UnsafeMod rhs) const { return UnsafeMod(*this) += rhs; } UnsafeMod operator - (UnsafeMod rhs) const { return UnsafeMod(*this) -= rhs; } UnsafeMod operator * (UnsafeMod rhs) const { return UnsafeMod(*this) *= rhs; } word_t get() const { return reduce(x) % mod; } void set(word_t n) { x = n; } UnsafeMod pow(word_t e) const { UnsafeMod ret = UnsafeMod(1); for (UnsafeMod base = *this; e; e >>= 1, base *= base) if (e & 1) ret *= base; return ret; } UnsafeMod inverse() const { return pow(mod - 2); } friend ostream& operator << (ostream& os, const UnsafeMod& m) { return os << m.get(); } static void debug() { printf("%llu %llu %llu %llu\n", mod, inv, r2, omega().get()); } word_t x; }; template void transform(mod_t* A, int n, const mod_t* roots, const mod_t* iroots) { const int logn = __builtin_ctz(n), nh = n >> 1, lv = mod_t::level; const mod_t one = mod_t(1), imag = roots[lv - 2]; mod_t dw[lv - 1]; dw[0] = roots[lv - 3]; for (int i = 1; i < lv - 2; ++i) dw[i] = dw[i - 1] * iroots[lv - 1 - i] * roots[lv - 3 - i]; dw[lv - 2] = dw[lv - 3] * iroots[1]; if (logn & 1) for (int i = 0; i < nh; ++i) { mod_t a = A[i], b = A[i + nh]; A[i] = a + b; A[i + nh] = a - b; } for (int e = logn & ~1; e >= 2; e -= 2) { const int m = 1 << e, m4 = m >> 2; mod_t w2 = one; for (int i = 0; i < n; i += m) { const mod_t w1 = w2 * w2, w3 = w1 * w2; for (int j = i; j < i + m4; ++j) { mod_t a0 = A[j + m4 * 0] * one, a1 = A[j + m4 * 1] * w2; mod_t a2 = A[j + m4 * 2] * w1, a3 = A[j + m4 * 3] * w3; mod_t t02p = a0 + a2, t13p = a1 + a3; mod_t t02m = a0 - a2, t13m = (a1 - a3) * imag; A[j + m4 * 0] = t02p + t13p; A[j + m4 * 1] = t02p - t13p; A[j + m4 * 2] = t02m + t13m; A[j + m4 * 3] = t02m - t13m; } w2 *= dw[__builtin_ctz(~(i >> e))]; } } } template void itransform(mod_t* A, int n, const mod_t* roots, const mod_t* iroots) { const int logn = __builtin_ctz(n), nh = n >> 1, lv = mod_t::level; const mod_t one = mod_t(1), imag = iroots[lv - 2]; mod_t dw[lv - 1]; dw[0] = iroots[lv - 3]; for (int i = 1; i < lv - 2; ++i) dw[i] = dw[i - 1] * roots[lv - 1 - i] * iroots[lv - 3 - i]; dw[lv - 2] = dw[lv - 3] * roots[1]; for (int e = 2; e <= logn; e += 2) { const int m = 1 << e, m4 = m >> 2; mod_t w2 = one; for (int i = 0; i < n; i += m) { const mod_t w1 = w2 * w2, w3 = w1 * w2; for (int j = i; j < i + m4; ++j) { mod_t a0 = A[j + m4 * 0], a1 = A[j + m4 * 1]; mod_t a2 = A[j + m4 * 2], a3 = A[j + m4 * 3]; mod_t t01p = a0 + a1, t23p = a2 + a3; mod_t t01m = a0 - a1, t23m = (a2 - a3) * imag; A[j + m4 * 0] = (t01p + t23p) * one; A[j + m4 * 2] = (t01p - t23p) * w1; A[j + m4 * 1] = (t01m + t23m) * w2; A[j + m4 * 3] = (t01m - t23m) * w3; } w2 *= dw[__builtin_ctz(~(i >> e))]; } } if (logn & 1) for (int i = 0; i < nh; ++i) { mod_t a = A[i], b = A[i + nh]; A[i] = a + b; A[i + nh] = a - b; } } template void convolve(mod_t* A, int s1, mod_t* B, int s2, bool cyclic=false) { const int s = cyclic ? max(s1, s2) : s1 + s2 - 1; const int size = 1 << (31 - __builtin_clz(2 * s - 1)); assert(size <= (i64(1) << mod_t::level)); mod_t roots[mod_t::level], iroots[mod_t::level]; roots[0] = mod_t::omega(); for (int i = 1; i < mod_t::level; ++i) roots[i] = roots[i - 1] * roots[i - 1]; iroots[0] = roots[0].inverse(); for (int i = 1; i < mod_t::level; ++i) iroots[i] = iroots[i - 1] * iroots[i - 1]; fill(A + s1, A + size, 0); transform(A, size, roots, iroots); const mod_t inv = mod_t(size).inverse(); if (A == B && s1 == s2) { for (int i = 0; i < size; ++i) A[i] *= A[i] * inv; } else { fill(B + s2, B + size, 0); transform(B, size, roots, iroots); for (int i = 0; i < size; ++i) A[i] *= B[i] * inv; } itransform(A, size, roots, iroots); } const int alloc_size = 1 << 17; using m64 = ntt::UnsafeMod<1128298388379402241, 23>; // <= 1.14e18 (sub.D = 3) m64 f[alloc_size], g[alloc_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::convolve(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; }