#include #include #include #include #define getchar getchar_unlocked #define putchar putchar_unlocked using namespace std; typedef long long int64; typedef long long unsigned uint64; typedef long double float80; typedef unsigned short uint16; typedef unsigned uint; typedef unsigned char uint8; uint get_uint() { uint n; int c; while( (c = getchar()) < '0') { ; } n = c - '0'; while( (c = getchar()) >= '0') { n = n * 10 + (c - '0'); } return n; } void put_uint(uint n) { uint8 stack[30]; int top = 0; do { stack[top++] = n % 10 + '0'; n /= 10; } while(n != 0); while(top > 0) { putchar(stack[--top]); } putchar('\n'); } typedef double real_t; template class Complex { public: Complex() {} Complex(const real_t a) : real_(a), imag_(0) {} Complex(const real_t a, const real_t b) : real_(a), imag_(b) {} Complex(const Complex& t) : real_(t.real_), imag_(t.imag_) {} Complex operator+(Complex rhs) const { Complex ret = Complex(*this); ret.real_ += rhs.real_; ret.imag_ += rhs.imag_; return ret; } Complex operator-(Complex rhs) const { Complex ret = Complex(*this); ret.real_ -= rhs.real_; ret.imag_ -= rhs.imag_; return ret; } Complex operator*(Complex rhs) const { Complex ret = Complex( real_ * rhs.real_ - imag_ * rhs.imag_, real_ * rhs.imag_ + imag_ * rhs.real_ ); return ret; } Complex operator*(const real_t rhs) const { Complex ret = Complex(*this); ret.real_ *= rhs; ret.imag_ *= rhs; return ret; } Complex operator+=(const Complex rhs) { return *this = *this + rhs; } Complex operator-=(const Complex rhs) { return *this = *this - rhs; } Complex operator*=(const Complex rhs) { return *this = *this * rhs; } Complex operator*=(const real_t rhs) { return *this = *this * rhs; } real_t real() const { return real_; } real_t imag() const { return imag_; } private: real_t real_, imag_; }; typedef Complex complex_t; class FFT { private: static constexpr real_t PI = acosl(-1); FFT() {} public: static void convolute_reals(real_t* A, const uint size_a, real_t* B, const uint size_b) { uint size = std::max(size_a, size_b); uint ldn = 0; uint fft_size = 1; while (fft_size < size) { ++ldn; fft_size <<= 1; } ++ldn; fft_size <<= 1; std::fill(A + size_a, A + fft_size, real_t(0)); std::fill(B + size_b, B + fft_size, real_t(0)); real_to_complex_fft(A, ldn); real_to_complex_fft(B, ldn); for (uint i = 1; i < fft_size / 2; ++i) { complex_t a = complex_t(A[2 * i], A[2 * i + 1]); complex_t b = complex_t(B[2 * i], B[2 * i + 1]); a *= b; A[2 * i + 0] = a.real(); A[2 * i + 1] = a.imag(); } A[0] *= B[0]; if (fft_size > 1) { A[1] *= B[1]; } complex_to_real_fft(A, ldn); real_t inv = 1. / fft_size; for (uint i = 0; i < fft_size; ++i) { A[i] *= inv; } } static void convolute(complex_t* A, const uint size_a, complex_t* B, const uint size_b) { uint size = std::max(size_a, size_b); uint ldn = 0; uint fft_size = 1; while (fft_size < size) { ++ldn; fft_size <<= 1; } ++ldn; fft_size <<= 1; std::fill(A + size_a, A + fft_size, complex_t(0)); std::fill(B + size_b, B + fft_size, complex_t(0)); fft_dit4(A, ldn, 1); fft_dit4(B, ldn, 1); for (uint i = 0; i < fft_size; ++i) { A[i] *= B[i]; } fft_dit4(A, ldn, -1); real_t inv = real_t(1) / fft_size; for (uint i = 0; i < fft_size; ++i) { A[i] *= inv; } } static void fft_dit4(complex_t *f, uint ldn, int sign) { const uint LX = 2; const uint n = 1u << ldn; revbin_permute(f, n); if (ldn & 1) { for (uint r = 0; r < n; r += 2) { sumdiff(f[r], f[r + 1]); } } uint ldm = LX + (ldn & 1); for (; ldm <= ldn; ldm += LX) { uint m = 1u << ldm; uint m4 = m >> LX; real_t ph0 = (2.0 * PI * sign) / m; for (uint j = 0; j < m4; ++j) { real_t phi = j * ph0; real_t s, c; sin_cos(phi, s, c); complex_t e = complex_t(c, s); complex_t e2 = e * e; complex_t e3 = e2 * e; for (uint r = 0; r < n; r += m) { const uint i = j + r; complex_t a0 = f[i + m4 * 0]; complex_t a2 = f[i + m4 * 1] * e2; complex_t a1 = f[i + m4 * 2] * e; complex_t a3 = f[i + m4 * 3] * e3; complex_t t02 = a0 + a2; complex_t t13 = a1 + a3; f[i + m4 * 0] = t02 + t13; f[i + m4 * 2] = t02 - t13; t02 = a0 - a2; t13 = (a1 - a3) * complex_t(0, sign); f[i + m4 * 1] = t02 + t13; f[i + m4 * 3] = t02 - t13; } } } } private: static void sin_cos(const real_t rad, real_t& s, real_t& c) { s = sin(rad); c = cos(rad); } static void real_to_complex_fft(real_t* f, uint ldn) { if (ldn == 0) { return; } fft_dit4((complex_t*)f, ldn - 1, 1); const uint n = 1u << ldn; const uint mh = n / 2, n4 = n / 4; const real_t phi0 = PI / mh; // before: // - F(a + bi) = c_s - d_a + i * (c_a + d_s) // // after: // - F(a + bz) = c_s + d_s * cos - d_a * sin // + i * (c_a + d_s * sin + d_a * cos) for (uint i = 1; i < n4; ++i) { uint i1 = 2 * i; uint i3 = n - i1; real_t r_k = f[i1 + 0], r_nk = f[i3 + 0]; sumdiff05(r_nk, r_k); // r_nk = c_s, r_k = d_a real_t i_k = f[i1 + 1], i_nk = f[i3 + 1]; sumdiff05(i_k, i_nk); // i_k = d_s, i_nk = c_a real_t phi = i * phi0; real_t s, c; sin_cos(phi, s, c); // i_k = d_s * cos - d_a * sin // r_k = d_s * sin + d_a * cos cmult(c, s, i_k, r_k); f[i1 + 0] = r_nk + i_k; f[i3 + 0] = r_nk - i_k; f[i1 + 1] = i_nk + r_k; f[i3 + 1] = -i_nk + r_k; } sumdiff(f[0], f[1]); } static void complex_to_real_fft(real_t* f, uint ldn) { if (ldn == 0) { return; } const uint n = 1u << ldn; const uint nh = n / 2, n4 = n / 4; const real_t phi0 = -PI / nh; // before: // - F(a - bi) = c_s + d_a + i * (c_a - d_s) // // after: // - F(a + bz^{-1}) = c_s + d_s * cos + d_a * sin // + i * (c_a - d_s * sin + d_a * cos) // for (uint i = 1; i < n4; ++i) { uint i1 = 2 * i; uint i3 = n - i1; real_t r_k = f[i1 + 0], r_nk = f[i3 + 0]; sumdiff(r_k, r_nk); // r_k = c_s, r_nk = d_a real_t i_k = -f[i1 + 1], i_nk = f[i3 + 1]; sumdiff(i_k, i_nk); // i_k = -c_a, i_nk = d_s real_t phi = i * phi0; real_t s, c; sin_cos(phi, s, c); // cos, -sin // i_nk = d_s * cos + d_a * sin // r_nk = -d_s * sin + d_a * cos cmult(c, s, i_nk, r_nk); f[i1 + 0] = r_k + i_nk; f[i3 + 0] = r_k - i_nk; f[i1 + 1] = -i_k + r_nk; f[i3 + 1] = i_k + r_nk; } sumdiff(f[0], f[1]); if (nh >= 2) { f[nh] *= 2.0; f[nh + 1] *= 2.0; } fft_dit4((complex_t*)f, ldn - 1, -1); } static inline void cmult(real_t c, real_t s, real_t& u, real_t& v) { real_t t = u * s + v * c; u *= c; u -= v * s; v = t; } template static inline void sumdiff05(T& a, T& b) { T t = (a - b) * 0.5; a += b; a *= 0.5; b = t; } template static inline void sumdiff(T& a, T& b) { T t = a - b; a += b; b = t; } template static void revbin_permute(T* A, uint n) { if(n <= 2) { return; } uint r = 0; uint nh = n >> 1; for(uint x = 1; x < n; ++x) { uint h = nh; while(! ((r ^= h) & h)) { h >>= 1; } if(r > x) { std::swap(A[x], A[r]); } } } }; real_t A[1 << 17]; real_t B[1 << 17]; uint res[200011]; int main() { uint L = get_uint(); uint M = get_uint(); uint N = get_uint(); const uint BASE = 100002; for (uint i = 0; i < L; ++i) { uint n = get_uint(); A[n / 2] += (n & 1 ? BASE : 1); } for (uint i = 0; i < M; ++i) { uint n = N - get_uint(); B[n / 2] += (n & 1 ? BASE : 1); } // 2n real => n complex FFT FFT::convolute_reals(A, N / 2 + 1, B, N / 2 + 1); uint Q = get_uint(); uint carry = 0; for (uint i = max(0, int(N / 2) - 1); i < (N + Q + 1) / 2; ++i) { uint64 n = uint64(A[i] + 0.41) + carry; // severe res[2 * i + 0] = n % BASE; n /= BASE; res[2 * i + 1] = n % BASE; carry = n / BASE; } for (uint i = N; i < N + Q; ++i) { put_uint(res[i]); } return 0; }