#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 1000000007; // constexpr int MOD = 998244353; constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct FPS { using MUL = std::function(const std::vector&, const std::vector&)>; using SQR = std::function; std::vector co; FPS(int deg = 0) : co(deg + 1, 0) {} FPS(const std::vector &co) : co(co) {} FPS(std::initializer_list init) : co(init.begin(), init.end()) {} template FPS(InputIter first, InputIter last) : co(first, last) {} inline const T &operator[](int term) const { return co[term]; } inline T &operator[](int term) { return co[term]; } static void set_mul(MUL mul) { get_mul() = mul; } static void set_sqr(SQR sqr) { get_sqr() = sqr; } void resize(int deg) { co.resize(deg + 1, 0); } void shrink() { while (co.size() > 1 && co.back() == 0) co.pop_back(); } int degree() const { return static_cast(co.size()) - 1; } FPS &operator=(const std::vector &new_co) { co.resize(new_co.size()); std::copy(new_co.begin(), new_co.end(), co.begin()); return *this; } FPS &operator=(const FPS &x) { co.resize(x.co.size()); std::copy(x.co.begin(), x.co.end(), co.begin()); return *this; } FPS &operator+=(const FPS &x) { int n = x.co.size(); if (n > co.size()) resize(n - 1); for (int i = 0; i < n; ++i) co[i] += x.co[i]; return *this; } FPS &operator-=(const FPS &x) { int n = x.co.size(); if (n > co.size()) resize(n - 1); for (int i = 0; i < n; ++i) co[i] -= x.co[i]; return *this; } FPS &operator*=(T x) { for (T &e : co) e *= x; return *this; } FPS &operator*=(const FPS &x) { return *this = get_mul()(co, x.co); } FPS &operator/=(T x) { assert(x != 0); T inv_x = static_cast(1) / x; for (T &e : co) e *= inv_x; return *this; } FPS &operator/=(const FPS &x) { int sz = x.co.size(); if (sz > co.size()) return *this = FPS(); int n = co.size() - sz + 1; FPS a(co.rbegin(), co.rbegin() + n), b(x.co.rbegin(), x.co.rbegin() + std::min(sz, n)); b = b.inv(n - 1); a *= b; return *this = FPS(a.co.rend() - n, a.co.rend()); } FPS &operator%=(const FPS &x) { *this -= *this / x * x; co.resize(static_cast(x.co.size()) - 1); if (co.empty()) co = {0}; return *this; } FPS &operator<<=(int n) { co.insert(co.begin(), n, 0); return *this; } FPS &operator>>=(int n) { if (co.size() < n) return *this = FPS(); co.erase(co.begin(), co.begin() + n); return *this; } bool operator==(const FPS &x) const { FPS a(*this), b(x); a.shrink(); b.shrink(); int n = a.co.size(); if (n != b.co.size()) return false; for (int i = 0; i < n; ++i) if (a.co[i] != b.co[i]) return false; return true; } bool operator!=(const FPS &x) const { return !(*this == x); } FPS operator+() const { return *this; } FPS operator-() const { FPS res(*this); for (T &e : res.co) e = -e; return res; } FPS operator+(const FPS &x) const { return FPS(*this) += x; } FPS operator-(const FPS &x) const { return FPS(*this) -= x; } FPS operator*(T x) const { return FPS(*this) *= x; } FPS operator*(const FPS &x) const { return FPS(*this) *= x; } FPS operator/(T x) const { return FPS(*this) /= x; } FPS operator/(const FPS &x) const { return FPS(*this) /= x; } FPS operator%(const FPS &x) const { return FPS(*this) %= x; } FPS operator<<(int n) const { return FPS(*this) <<= n; } FPS operator>>(int n) const { return FPS(*this) >>= n; } T horner(T val) const { T res = 0; for (int i = static_cast(co.size()) - 1; i >= 0; --i) (res *= val) += co[i]; return res; } FPS differential() const { int n = co.size(); assert(n >= 1); FPS res(n - 1); for (int i = 1; i < n; ++i) res.co[i - 1] = co[i] * i; return res; } FPS integral() const { int n = co.size(); FPS res(n + 1); for (int i = 0; i < n; ++i) res[i + 1] = co[i] / (i + 1); return res; } FPS exp(int deg = -1) const { assert(co[0] == 0); int n = co.size(); if (deg == -1) deg = n - 1; FPS one{1}, res = one; for (int i = 1; i <= deg; i <<= 1) { res *= FPS(co.begin(), co.begin() + std::min(n, i << 1)) - res.log((i << 1) - 1) + one; res.co.resize(i << 1); } res.co.resize(deg + 1); return res; } FPS inv(int deg = -1) const { assert(co[0] != 0); int n = co.size(); if (deg == -1) deg = n - 1; FPS res{static_cast(1) / co[0]}; for (int i = 1; i <= deg; i <<= 1) { res = res + res - res * res * FPS(co.begin(), co.begin() + std::min(n, i << 1)); res.co.resize(i << 1); } res.co.resize(deg + 1); return res; } FPS log(int deg = -1) const { assert(co[0] == 1); if (deg == -1) deg = static_cast(co.size()) - 1; FPS integrand = differential() * inv(deg - 1); integrand.co.resize(deg); return integrand.integral(); } FPS pow(long long exponent, int deg = -1) const { int n = co.size(); if (deg == -1) deg = n - 1; for (int i = 0; i < n; ++i) { if (co[i] != 0) { long long shift = exponent * i; if (shift > deg) break; T tmp = 1, base = co[i]; long long e = exponent; while (e > 0) { if (e & 1) tmp *= base; base *= base; e >>= 1; } return ((((*this >> i) * (static_cast(1) / co[i])).log(deg - shift) * static_cast(exponent)).exp(deg - shift) * tmp) << shift; } } return FPS(deg); } FPS mod_pow(long long exponent, const FPS &md) const { FPS inv_rev_md = FPS(md.co.rbegin(), md.co.rend()).inv(); int deg_of_md = md.co.size(); auto mod_mul = [&](FPS &multiplicand, const FPS &multiplier) -> void { multiplicand *= multiplier; if (deg_of_md <= multiplicand.co.size()) { int n = multiplicand.co.size() - deg_of_md + 1; FPS quotient = FPS(multiplicand.co.rbegin(), multiplicand.co.rbegin() + n) * FPS(inv_rev_md.co.begin(), inv_rev_md.co.begin() + std::min(static_cast(inv_rev_md.co.size()), n)); multiplicand -= FPS(quotient.co.rend() - n, quotient.co.rend()) * md; } multiplicand.co.resize(deg_of_md - 1); if (multiplicand.co.empty()) multiplicand.co = {0}; }; FPS res{1}, base = *this; mod_mul(base, res); while (exponent > 0) { if (exponent & 1) mod_mul(res, base); mod_mul(base, base); exponent >>= 1; } return res; } FPS sqrt(int deg = -1) const { int n = co.size(); if (deg == -1) deg = n - 1; if (co[0] == 0) { for (int i = 1; i < n; ++i) { if (co[i] == 0) continue; if (i & 1) return FPS(-1); int shift = i >> 1; if (deg < shift) break; FPS res = (*this >> i).sqrt(deg - shift); if (res.co.empty()) return FPS(-1); res <<= shift; res.resize(deg); return res; } return FPS(deg); } T s; if (!get_sqr()(co[0], s)) return FPS(-1); FPS res{s}; T half = static_cast(1) / 2; for (int i = 1; i <= deg; i <<= 1) { (res += FPS(co.begin(), co.begin() + std::min(n, i << 1)) * res.inv((i << 1) - 1)) *= half; } res.resize(deg); return res; } FPS translate(T c) const { int n = co.size(); std::vector fact(n, 1), inv_fact(n, 1); for (int i = 1; i < n; ++i) fact[i] = fact[i - 1] * i; inv_fact[n - 1] = static_cast(1) / fact[n - 1]; for (int i = n - 1; i > 0; --i) inv_fact[i - 1] = inv_fact[i] * i; std::vector g(n), ex(n); for (int i = 0; i < n; ++i) g[n - 1 - i] = co[i] * fact[i]; T pow_c = 1; for (int i = 0; i < n; ++i) { ex[i] = pow_c * inv_fact[i]; pow_c *= c; } std::vector conv = get_mul()(g, ex); FPS res(n - 1); for (int i = 0; i < n; ++i) res[i] = conv[n - 1 - i] * inv_fact[i]; return res; } private: static MUL &get_mul() { static MUL mul = [](const std::vector &a, const std::vector &b) -> std::vector { int n = a.size(), m = b.size(); std::vector res(n + m - 1, 0); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) res[i + j] += a[i] * b[j]; return res; }; return mul; } static SQR &get_sqr() { static SQR sqr = [](const T &a, T &res) -> bool { return false; }; return sqr; } }; namespace fft { using Real = double; struct Complex { Real re, im; Complex(Real re = 0, Real im = 0) : re(re), im(im) {} inline Complex operator+(const Complex &x) const { return Complex(re + x.re, im + x.im); } inline Complex operator-(const Complex &x) const { return Complex(re - x.re, im - x.im); } inline Complex operator*(const Complex &x) const { return Complex(re * x.re - im * x.im, re * x.im + im * x.re); } inline Complex mul_real(Real r) const { return Complex(re * r, im * r); } inline Complex mul_pin(Real r) const { return Complex(-im * r, re * r); } inline Complex conj() const { return Complex(re, -im); } }; std::vector butterfly{0}; std::vector> zeta{{{1, 0}}}; void calc(int n) { int prev_n = butterfly.size(); if (n <= prev_n) return; butterfly.resize(n); int prev_lg = zeta.size(), lg = __builtin_ctz(n); for (int i = 1; i < prev_n; ++i) butterfly[i] <<= lg - prev_lg; for (int i = prev_n; i < n; ++i) butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1)); zeta.resize(lg); for (int i = prev_lg; i < lg; ++i) { zeta[i].resize(1 << i); Real angle = -3.14159265358979323846 * 2 / (1 << (i + 1)); for (int j = 0; j < (1 << (i - 1)); ++j) { zeta[i][j << 1] = zeta[i - 1][j]; Real theta = angle * ((j << 1) + 1); zeta[i][(j << 1) + 1] = {std::cos(theta), std::sin(theta)}; } } } void sub_dft(std::vector &a) { int n = a.size(); assert(__builtin_popcount(n) == 1); calc(n); int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n); for (int i = 0; i < n; ++i) { int j = butterfly[i] >> shift; if (i < j) std::swap(a[i], a[j]); } for (int block = 1; block < n; block <<= 1) { int den = __builtin_ctz(block); for (int i = 0; i < n; i += (block << 1)) for (int j = 0; j < block; ++j) { Complex tmp = a[i + j + block] * zeta[den][j]; a[i + j + block] = a[i + j] - tmp; a[i + j] = a[i + j] + tmp; } } } template std::vector dft(const std::vector &a) { int sz = a.size(), lg = 1; while ((1 << lg) < sz) ++lg; std::vector c(1 << lg); for (int i = 0; i < sz; ++i) c[i].re = a[i]; sub_dft(c); return c; } std::vector real_idft(std::vector &a) { int n = a.size(), half = n >> 1, quarter = half >> 1; assert(__builtin_popcount(n) == 1); calc(n); a[0] = (a[0] + a[half] + (a[0] - a[half]).mul_pin(1)).mul_real(0.5); int den = __builtin_ctz(half); for (int i = 1; i < quarter; ++i) { int j = half - i; Complex tmp1 = a[i] + a[j].conj(), tmp2 = ((a[i] - a[j].conj()) * zeta[den][j]).mul_pin(1); a[i] = (tmp1 - tmp2).mul_real(0.5); a[j] = (tmp1 + tmp2).mul_real(0.5).conj(); } if (quarter > 0) a[quarter] = a[quarter].conj(); a.resize(half); sub_dft(a); std::reverse(a.begin() + 1, a.end()); Real r = 1.0 / half; std::vector res(n); for (int i = 0; i < n; ++i) res[i] = (i & 1 ? a[i >> 1].im : a[i >> 1].re) * r; return res; } void idft(std::vector &a) { int n = a.size(); sub_dft(a); std::reverse(a.begin() + 1, a.end()); Real r = 1.0 / n; for (int i = 0; i < n; ++i) a[i] = a[i].mul_real(r); } template std::vector convolution(const std::vector &a, const std::vector &b) { int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1; while ((1 << lg) < sz) ++lg; int n = 1 << lg; std::vector c(n); for (int i = 0; i < a_sz; ++i) c[i].re = a[i]; for (int i = 0; i < b_sz; ++i) c[i].im = b[i]; sub_dft(c); c[0] = Complex(c[0].re * c[0].im, 0); int half = n >> 1; for (int i = 1; i < half; ++i) { Complex i_square = c[i] * c[i], j_square = c[n - i] * c[n - i]; c[i] = (j_square.conj() - i_square).mul_pin(0.25); c[n - i] = (i_square.conj() - j_square).mul_pin(0.25); } c[half] = Complex(c[half].re * c[half].im, 0); std::vector res = real_idft(c); res.resize(sz); return res; } } // fft int main() { FPS::set_mul([](const vector &a, const vector &b) { vector f = fft::convolution(a, b); int n = f.size(); vector c(n); REP(i, n) c[i] = static_cast(round(f[i])); return c; }); int n, q; cin >> n >> q; FPS a(n - 1), r(n - 1); REP(i, n) cin >> a[n - 1 - i]; // REP(i, n) cout << a[i] << " \n"[i + 1 == n]; while (q--) { int ri; cin >> ri; ++r[ri]; } // REP(i, n) cout << r[i] << " \n"[i + 1 == n]; a *= r; vector ans(n, 0); REP(i, a.degree() + 1) ans[i % n] += a[i]; reverse(ALL(ans)); REP(i, n) cout << ans[i] << " \n"[i + 1 == n]; return 0; }