#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template S SUM(const vector &a) { return accumulate(ALL(a), S(0)); } template S POW(S a, T b) { S ret = 1, base = a; for (;;) { if (b & 1) ret *= base; b >>= 1; if (b == 0) break; base *= base; } return ret; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template int popcnt(T x) { return __builtin_popcountll(x); } template int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template ostream &operator<<(ostream &os, const pair &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template ostream &operator<<(ostream &os, const vector &vec) { os << "{"; for (int i = 0; i < vec.size(); i++) { os << vec[i] << (i + 1 == vec.size() ? "" : ", "); } os << "}"; return os; } template ostream &operator<<(ostream &os, const map &map_var) { os << "{"; for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << "(" << itr->first << ", " << itr->second << ")"; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } #ifdef LOCAL #define debug 1 #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define debug 0 #define show(...) true #endif template void _show(int i, T name) { cerr << '\n'; } template void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } #line 2 "library/Utility/fastio.hpp" #include namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memmove(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(uint &x) { rd_integer(x); } void rd(ull &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d : x) rd(d); } template void rd(vector &x) { for (auto &d : x) rd(d); } void read() {} template void read(H &h, T &...t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c : s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(uint x) { wt_integer(x); } void wt(ull x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&...tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; inline void first(bool i = true) { print(i ? "first" : "second"); } inline void Alice(bool i = true) { print(i ? "Alice" : "Bob"); } inline void Takahashi(bool i = true) { print(i ? "Takahashi" : "Aoki"); } inline void yes(bool i = true) { print(i ? "yes" : "no"); } inline void Yes(bool i = true) { print(i ? "Yes" : "No"); } inline void No() { print("No"); } inline void YES(bool i = true) { print(i ? "YES" : "NO"); } inline void NO() { print("NO"); } inline void Yay(bool i = true) { print(i ? "Yay!" : ":("); } inline void Possible(bool i = true) { print(i ? "Possible" : "Impossible"); } inline void POSSIBLE(bool i = true) { print(i ? "POSSIBLE" : "IMPOSSIBLE"); } /** * @brief Fast IO */ #line 2 "library/Utility/random.hpp" namespace Random { mt19937_64 randgen(chrono::steady_clock::now().time_since_epoch().count()); using u64 = unsigned long long; u64 get() { return randgen(); } template T get(T L) { // [0,L] return get() % (L + 1); } template T get(T L, T R) { // [L,R] return get(R - L) + L; } double uniform() { return double(get(1000000000)) / 1000000000; } string str(int n) { string ret; rep(i, 0, n) ret += get('a', 'z'); return ret; } template void shuffle(Iter first, Iter last) { if (first == last) return; int len = 1; for (auto it = first + 1; it != last; it++) { len++; int j = get(0, len - 1); if (j != len - 1) iter_swap(it, first + j); } } template vector select(int n, T L, T R) { // [L,R] if (n * 2 >= R - L + 1) { vector ret(R - L + 1); iota(ALL(ret), L); shuffle(ALL(ret)); ret.resize(n); return ret; } else { unordered_set used; vector ret; while (SZ(used) < n) { T x = get(L, R); if (!used.count(x)) { used.insert(x); ret.push_back(x); } } return ret; } } void relabel(int n, vector> &es) { shuffle(ALL(es)); vector ord(n); iota(ALL(ord), 0); shuffle(ALL(ord)); for (auto &[u, v] : es) u = ord[u], v = ord[v]; } template vector> genGraph(int n, int m) { vector> cand, es; rep(u, 0, n) rep(v, 0, n) { if (!self and u == v) continue; if (!directed and u > v) continue; cand.push_back({u, v}); } if (m == -1) m = get(SZ(cand)); // chmin(m, SZ(cand)); vector ord; if (multi) rep(_, 0, m) ord.push_back(get(SZ(cand) - 1)); else { ord = select(m, 0, SZ(cand) - 1); } for (auto &i : ord) es.push_back(cand[i]); relabel(n, es); return es; } vector> genTree(int n) { vector> es; rep(i, 1, n) es.push_back({get(i - 1), i}); relabel(n, es); return es; } }; // namespace Random /** * @brief Random */ #line 4 "sol.cpp" #line 2 "library/Math/fastdiv.hpp" struct FastDiv { using u64 = uint64_t; using u128 = __uint128_t; constexpr FastDiv() : m(), s(), x() {} constexpr FastDiv(int _m) : m(_m), s(__lg(m - 1)), x(((u128(1) << (s + 64)) + m - 1) / m) {} constexpr int get() { return m; } constexpr friend u64 operator/(u64 n, const FastDiv &d) { return (u128(n) * d.x >> d.s) >> 64; } constexpr friend int operator%(u64 n, const FastDiv &d) { return n - n / d * d.m; } constexpr pair divmod(u64 n) const { u64 q = n / (*this); return {q, n - q * m}; } int m, s; u64 x; }; struct FastDiv64 { using u64 = uint64_t; using u128 = __uint128_t; u128 mod, mh, ml; explicit FastDiv64(u64 mod = 1) : mod(mod) { u128 m = u128(-1) / mod; if (m * mod + mod == u128(0)) ++m; mh = m >> 64; ml = m & u64(-1); } u64 umod() const { return mod; } u64 modulo(u128 x) { u128 z = (x & u64(-1)) * ml; z = (x & u64(-1)) * mh + (x >> 64) * ml + (z >> 64); z = (x >> 64) * mh + (z >> 64); x -= z * mod; return x < mod ? x : x - mod; } u64 mul(u64 a, u64 b) { return modulo(u128(a) * b); } }; /** * @brief Fast Division */ #line 2 "library/Math/comb.hpp" template T Inv(ll n) { static int md; static vector buf({0, 1}); if (md != T::get_mod()) { md = T::get_mod(); buf = vector({0, 1}); } assert(n > 0); n %= md; while (SZ(buf) <= n) { int k = SZ(buf), q = (md + k - 1) / k; buf.push_back(buf[k * q - md] * q); } return buf[n]; } template T Fact(ll n, bool inv = 0) { static int md; static vector buf({1, 1}), ibuf({1, 1}); if (md != T::get_mod()) { md = T::get_mod(); buf = ibuf = vector({1, 1}); } assert(n >= 0 and n < md); while (SZ(buf) <= n) { buf.push_back(buf.back() * SZ(buf)); ibuf.push_back(ibuf.back() * Inv(SZ(ibuf))); } return inv ? ibuf[n] : buf[n]; } template T nPr(int n, int r, bool inv = 0) { if (n < 0 || n < r || r < 0) return 0; return Fact(n, inv) * Fact(n - r, inv ^ 1); } template T nCr(int n, int r, bool inv = 0) { if (n < 0 || n < r || r < 0) return 0; return Fact(n, inv) * Fact(r, inv ^ 1) * Fact(n - r, inv ^ 1); } // sum = n, r tuples template T nHr(int n, int r, bool inv = 0) { return nCr(n + r - 1, r - 1, inv); } // [x^n]C(x)^k template T Catalan(int n, int k) { if (k == 0) return (n == 0 ? 1 : 0); return T(k) * Inv(n * 2 + k) * nCr(n * 2 + k, n); } // sum = n, a nonzero tuples and b tuples template T choose(int n, int a, int b) { if (n == 0) return !a; return nCr(n + b - 1, a + b - 1); } /** * @brief Combination */ #line 4 "library/Math/dynamic.hpp" struct Fp { using u64 = uint64_t; uint v; static uint get_mod() { return _getmod(); } static void set_mod(uint _m) { bar = FastDiv(_m); } Fp inv() const { int tmp, a = v, b = get_mod(), x = 1, y = 0; while (b) { tmp = a / b, a -= tmp * b; swap(a, b); x -= tmp * y; swap(x, y); } if (x < 0) { x += get_mod(); } return x; } Fp() : v(0) {} Fp(ll x) { v = (x % get_mod() + get_mod()) % get_mod(); } Fp operator-() const { return Fp() - *this; } Fp pow(ll t) { assert(t >= 0); Fp res = 1, b = *this; while (t) { if (t & 1) res *= b; b *= b; t >>= 1; } return res; } Fp &operator+=(const Fp &x) { v += x.v; if (v >= get_mod()) v -= get_mod(); return *this; } Fp &operator-=(const Fp &x) { v += get_mod() - x.v; if (v >= get_mod()) v -= get_mod(); return *this; } Fp &operator*=(const Fp &x) { v = (u64(v) * x.v) % bar; return *this; } Fp &operator/=(const Fp &x) { (*this) *= x.inv(); return *this; } Fp operator+(const Fp &x) const { return Fp(*this) += x; } Fp operator-(const Fp &x) const { return Fp(*this) -= x; } Fp operator*(const Fp &x) const { return Fp(*this) *= x; } Fp operator/(const Fp &x) const { return Fp(*this) /= x; } bool operator==(const Fp &x) const { return v == x.v; } bool operator!=(const Fp &x) const { return v != x.v; } friend istream &operator>>(istream &is, Fp &x) { return is >> x.v; } friend ostream &operator<<(ostream &os, const Fp &x) { return os << x.v; } private: static FastDiv bar; static uint _getmod() { return bar.get(); } }; FastDiv Fp::bar(998244353); void rd(Fp &x) { fastio::rd(x.v); } void wt(Fp x) { fastio::wt(x.v); } /** * @brief Dynamic Modint */ #line 6 "sol.cpp" int main() { int n, P; ll m; read(n, m, P); Fp::set_mod(P); vector a(n + 1); rep(i, 1, n + 1) { ll x; read(x); a[i] = Fp(x); } // arctan vector b(n + 1); { vector num(n + 1), den(n + 1); rep(i, 0, n) num[i] = a[i + 1] * (i + 1); den[0] = 1; rep(i, 0, n + 1) { rep(j, 0, n + 1) { if (i + j > n) break; den[i + j] += a[i] * a[j]; } } vector db(n + 1); rep(i, 0, n + 1) { db[i] = num[i]; rep(j, 0, i) { db[i] -= db[j] * den[i - j]; } } rep(i, 0, n) b[i + 1] = db[i] * Inv(i + 1); } // *m rep(i, 0, n + 1) b[i] *= m; show(b); // tan vector ret(n + 1); { vector db(n); rep(i, 0, n) db[i] = b[i + 1] * (i + 1); vector ret2(n + 1); ret2[0] = 1; rep(k, 1, n + 1) { rep(i, 0, k) { ret[k] += db[i] * ret2[k - 1 - i]; } ret[k] *= Inv(k); if (k * 2 <= n) ret2[k * 2] += ret[k] * ret[k]; rep(i, 0, k) if (k + i <= n) ret2[k + i] += ret[k] * ret[i] * 2; } } ret.erase(ret.begin()); print(ret); return 0; }