結果
| 問題 | No.2720 Sum of Subarray of Subsequence of... |
| ユーザー |
👑  binap
|
| 提出日時 | 2024-04-06 20:40:22 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 494 ms / 4,000 ms |
| コード長 | 22,374 bytes |
| コンパイル時間 | 5,402 ms |
| コンパイル使用メモリ | 274,688 KB |
| 最終ジャッジ日時 | 2025-02-20 22:38:39 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 31 |
ソースコード
#include<bits/stdc++.h>#include<atcoder/all>#define rep(i,n) for(int i=0;i<n;i++)using namespace std;using namespace atcoder;typedef long long ll;typedef vector<int> vi;typedef vector<long long> vl;typedef vector<vector<int>> vvi;typedef vector<vector<long long>> vvl;typedef long double ld;typedef pair<int, int> P;ostream& operator<<(ostream& os, const modint& a) {os << a.val(); return os;}template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;}template <int m> ostream& operator<<(ostream& os, const dynamic_modint<m>& a) {os << a.val(); return os;}template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;}template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;}template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); returnos;}template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : "");return os;}template<typename T> void chmin(T& a, T b){a = min(a, b);}template<typename T> void chmax(T& a, T b){a = max(a, b);}using mint = modint998244353;// thanks for Nyaan-san's library// https://nyaannyaan.github.io/library/fps/formal-power-series.hpptemplate <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t _mod = mint::mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for (u64 i = 2; i * i <= m; ++i) {if (m % i == 0) {ds[idx++] = i;while (m % i == 0) m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while (1) {int flg = 1;for (int i = 0; i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;while (b) {if (b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if (r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];void setwy(int k) {mint w[level], y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inv();for (int i = k - 2; i > 0; --i)w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for (int i = 3; i < k; ++i) {dw[i] = dw[i - 1] * y[i - 2] * w[i];dy[i] = dy[i - 1] * w[i - 2] * y[i];}}NTT() { setwy(level); }void fft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for (int j = 0; j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while (v) {// jh = 0{int j0 = 0;int j1 = v;int j2 = j1 + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}// jh >= 1mint ww = one, xx = one * dw[2], wx = one;for (int jh = 4; jh < u;) {ww = xx * xx, wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while (u) {// jh = 0{int j0 = 0;int j1 = v;int j2 = v + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}// jh >= 1mint ww = one, xx = one * dy[2], yy = one;u <<= 2;for (int jh = 4; jh < u;) {ww = xx * xx, yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if (k & 1) {u = 1 << (k - 1);for (int j = 0; j < u; ++j) {mint ajv = a[j] - a[j + u];a[j] += a[j + u];a[j + u] = ajv;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;fft4(a, __builtin_ctz(a.size()));}void intt(vector<mint> &a) {if ((int)a.size() <= 1) return;ifft4(a, __builtin_ctz(a.size()));mint iv = mint(a.size()).inv();for (auto &x : a) x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<mint> s(l);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;setwy(k);vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];} else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inv();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}void ntt_doubling(vector<mint> &a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::mod() - 1) / (M << 1));for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;ntt(b);copy(begin(b), end(b), back_inserter(a));}};template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS &operator+=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}FPS &operator+=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}FPS &operator-=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const mint &v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS &operator/=(const FPS &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inv();for (auto &x : g) x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS &operator%=(const FPS &r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator+(const mint &v) const { return FPS(*this) += v; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator-(const mint &v) const { return FPS(*this) -= v; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator*(const mint &v) const { return FPS(*this) *= v; }FPS operator/(const FPS &r) const { return FPS(*this) /= r; }FPS operator%(const FPS &r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0)) this->pop_back();}FPS rev() const {FPS ret(*this);reverse(begin(ret), end(ret));return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}// 前 sz 項を取ってくる。sz に足りない項は 0 埋めするFPS pre(int sz) const {FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));if ((int)ret.size() < sz) ret.resize(sz);return ret;}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::mod();for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto &v : *this) r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert(!(*this).empty() && (*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}static void *ntt_ptr;static void set_fft();FPS &operator*=(const FPS &r);void ntt();void intt();void ntt_doubling();static int ntt_pr();FPS inv(int deg = -1) const;FPS exp(int deg = -1) const;};template <typename mint>void *FormalPowerSeries<mint>::ntt_ptr = nullptr;template <typename mint>void FormalPowerSeries<mint>::set_fft() {if (!ntt_ptr) ntt_ptr = new NTT<mint>;}template <typename mint>FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {if (this->empty() || r.empty()) {this->clear();return *this;}set_fft();auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>void FormalPowerSeries<mint>::ntt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);}template <typename mint>void FormalPowerSeries<mint>::intt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {set_fft();return static_cast<NTT<mint>*>(ntt_ptr)->pr;}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> res(deg);res[0] = {mint(1) / (*this)[0]};for (int d = 1; d < deg; d <<= 1) {FormalPowerSeries<mint> f(2 * d), g(2 * d);for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];for (int j = 0; j < d; j++) g[j] = res[j];f.ntt();g.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = 0; j < d; j++) f[j] = 0;f.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];}return res.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {using fps = FormalPowerSeries<mint>;assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = this->size();fps inv;inv.reserve(deg + 1);inv.push_back(mint(0));inv.push_back(mint(1));auto inplace_integral = [&](fps& F) -> void {const int n = (int)F.size();auto mod = mint::mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), mint(0));for (int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_diff = [](fps& F) -> void {if (F.empty()) return;F.erase(begin(F));mint coeff = 1, one = 1;for (int i = 0; i < (int)F.size(); i++) {F[i] *= coeff;coeff += one;}};fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for (int m = 2; m < deg; m *= 2) {auto y = b;y.resize(2 * m);y.ntt();z1 = z2;fps z(m);for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];z.intt();fill(begin(z), begin(z) + m / 2, mint(0));z.ntt();for (int i = 0; i < m; ++i) z[i] *= -z1[i];z.intt();c.insert(end(c), begin(z) + m / 2, end(z));z2 = c;z2.resize(2 * m);z2.ntt();fps x(begin(*this), begin(*this) + min<int>(this->size(), m));x.resize(m);inplace_diff(x);x.push_back(mint(0));x.ntt();for (int i = 0; i < m; ++i) x[i] *= y[i];x.intt();x -= b.diff();x.resize(2 * m);for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];x.intt();x.pop_back();inplace_integral(x);for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];fill(begin(x), begin(x) + m, mint(0));x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];x.intt();b.insert(end(b), begin(x) + m, end(x));}return fps{begin(b), begin(b) + deg};}// [x^n] f(x)^i g(x) を i=0,1,...,m で列挙// n = (f の次数) - 1template <typename mint>FormalPowerSeries<mint> pow_enumerate(FormalPowerSeries<mint> f,FormalPowerSeries<mint> g = {1},int m = -1) {using fps = FormalPowerSeries<mint>;int n = f.size() - 1, k = 1;g.resize(n + 1);if (m == -1) m = n;int h = 1;while (h < n + 1) h *= 2;fps P((n + 1) * k), Q((n + 1) * k), nP, nQ, buf, buf2;for (int i = 0; i <= n; i++) P[i * k + 0] = g[i];for (int i = 0; i <= n; i++) Q[i * k + 0] = -f[i];Q[0] += 1;while (n) {mint inv2 = mint{2}.inv();mint w = mint{fps::ntt_pr()}.pow((mint::mod() - 1) / (2 * k));mint iw = w.inv();buf2.resize(k);auto ntt_doubling = [&]() {copy(begin(buf), end(buf), begin(buf2));buf2.intt();mint c = 1;for (int i = 0; i < k; i++) buf2[i] *= c, c *= w;buf2.ntt();copy(begin(buf2), end(buf2), back_inserter(buf));};nP.clear(), nQ.clear();for (int i = 0; i <= n; i++) {buf.resize(k);copy(begin(P) + i * k, begin(P) + (i + 1) * k, begin(buf));ntt_doubling();copy(begin(buf), end(buf), back_inserter(nP));buf.resize(k);copy(begin(Q) + i * k, begin(Q) + (i + 1) * k, begin(buf));if (i == 0) {for (int j = 0; j < k; j++) buf[j] -= 1;ntt_doubling();for (int j = 0; j < k; j++) buf[j] += 1;for (int j = 0; j < k; j++) buf[k + j] -= 1;} else {ntt_doubling();}copy(begin(buf), end(buf), back_inserter(nQ));}nP.resize(2 * h * 2 * k);nQ.resize(2 * h * 2 * k);fps p(2 * h), q(2 * h);w = mint{fps::ntt_pr()}.pow((mint::mod() - 1) / (2 * h));iw = w.inv();vector<int> btr;if (n % 2) {btr.resize(h);for (int i = 0, lg = __builtin_ctz(h); i < h; i++) {btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (lg - 1));}}for (int j = 0; j < 2 * k; j++) {p.assign(2 * h, 0);q.assign(2 * h, 0);for (int i = 0; i < h; i++) {p[i] = nP[i * 2 * k + j], q[i] = nQ[i * 2 * k + j];}p.ntt(), q.ntt();for (int i = 0; i < 2 * h; i += 2) swap(q[i], q[i + 1]);for (int i = 0; i < 2 * h; i++) p[i] *= q[i];for (int i = 0; i < h; i++) q[i] = q[i * 2] * q[i * 2 + 1];if (n % 2 == 0) {for (int i = 0; i < h; i++) p[i] = (p[i * 2] + p[i * 2 + 1]) * inv2;} else {mint c = inv2;buf.resize(h);for (int i : btr) buf[i] = (p[i * 2] - p[i * 2 + 1]) * c, c *= iw;swap(p, buf);}p.resize(h), q.resize(h);p.intt(), q.intt();for (int i = 0; i < h; i++) nP[i * 2 * k + j] = p[i];for (int i = 0; i < h; i++) nQ[i * 2 * k + j] = q[i];}nP.resize((n / 2 + 1) * 2 * k);nQ.resize((n / 2 + 1) * 2 * k);swap(P, nP), swap(Q, nQ);n /= 2, h /= 2, k *= 2;}fps S{begin(P), begin(P) + k};fps T{begin(Q), begin(Q) + k};S.intt(), T.intt(), T[0] -= 1;if (f[0] == 0) return S.rev().pre(m + 1);return (S.rev() * (T + (fps{1} << k)).rev().inv(m + 1)).pre(m + 1);}// g(f(x)) を計算template <typename mint>FormalPowerSeries<mint> composition(FormalPowerSeries<mint> f,FormalPowerSeries<mint> g, int deg = -1) {using fps = FormalPowerSeries<mint>;auto dfs = [&](auto rc, fps Q, int n, int h, int k) -> fps {if (n == 0) {fps T{begin(Q), begin(Q) + k};T.push_back(1);fps u = g * T.rev().inv().rev();fps P(h * k);for (int i = 0; i < (int)g.size(); i++) P[k - 1 - i] = u[i + k];return P;}fps nQ(4 * h * k), nR(2 * h * k);for (int i = 0; i < k; i++) {copy(begin(Q) + i * h, begin(Q) + i * h + n + 1, begin(nQ) + i * 2 * h);}nQ[k * 2 * h] += 1;nQ.ntt();for (int i = 0; i < 4 * h * k; i += 2) swap(nQ[i], nQ[i + 1]);for (int i = 0; i < 2 * h * k; i++) nR[i] = nQ[i * 2] * nQ[i * 2 + 1];nR.intt();nR[0] -= 1;Q.assign(h * k, 0);for (int i = 0; i < 2 * k; i++) {for (int j = 0; j <= n / 2; j++) {Q[i * h / 2 + j] = nR[i * h + j];}}auto P = rc(rc, Q, n / 2, h / 2, k * 2);fps nP(4 * h * k);for (int i = 0; i < 2 * k; i++) {for (int j = 0; j <= n / 2; j++) {nP[i * 2 * h + j * 2 + n % 2] = P[i * h / 2 + j];}}nP.ntt();for (int i = 1; i < 4 * h * k; i *= 2) {reverse(begin(nQ) + i, begin(nQ) + i * 2);}for (int i = 0; i < 4 * h * k; i++) nP[i] *= nQ[i];nP.intt();P.assign(h * k, 0);for (int i = 0; i < k; i++) {copy(begin(nP) + i * 2 * h, begin(nP) + i * 2 * h + n + 1,begin(P) + i * h);}return P;};if (deg == -1) deg = max(f.size(), g.size());f.resize(deg), g.resize(deg);int n = f.size() - 1, k = 1;int h = 1;while (h < n + 1) h *= 2;fps Q(h * k);for (int i = 0; i <= n; i++) Q[i] = -f[i];fps P = dfs(dfs, Q, n, h, k);return P.pre(n + 1).rev();}// f を入力として, f(g(x)) = x を満たす g(x) mod x^{deg} を返すtemplate <typename mint>FormalPowerSeries<mint> compositional_inverse(FormalPowerSeries<mint> f,int deg = -1) {assert(int(f.size()) == deg);using fps = FormalPowerSeries<mint>;assert((int)f.size() >= 2 and f[1] != 0);if (deg == -1) deg = f.size();if (deg < 2) return fps{0, f[1].inv()}.pre(deg);int n = deg - 1;fps h = pow_enumerate(f) * n;for (int k = 1; k <= n; k++) h[k] /= k;h = h.rev();h *= h[0].inv();fps g = (h.log() * mint{-n}.inv()).exp();g *= f[1].inv();return (g << 1).pre(deg);}// f(g(x)) = x を満たす g(x) mod x^{deg} を返す// calc_f(g, d) は f(g(x)) mod x^d を計算する関数template <typename fps>fps compositional_inverse(function<fps(fps, int)> calc_f, int deg) {if (deg <= 2) {fps g = calc_f(fps{0, 1}, 2);assert(g[0] == 0 && g[1] != 0);g[1] = g[1].inv();return g.pre(deg);}fps g = compositional_inverse(calc_f, (deg + 1) / 2);fps fg = calc_f(g, deg + 1);fps fdg = (fg.diff() * g.diff().inv(deg)).pre(deg);return (g - (fg - fps{0, 1}) * fdg.inv()).pre(deg);}template<typename fps>struct Merge{int n;using P = fps;using Comp = std::function<bool(const P&, const P&)>;Comp comp = [](const P& a, const P& b){return a.size() > b.size();};priority_queue<P, vector<P>, Comp> pq;Merge(int n = -1) : n(n), pq(comp){pq.push(P{1});}void push(P r){pq.push(r);}P get(){while(pq.size() > 1){auto f = pq.top(); pq.pop();auto g = pq.top(); pq.pop();f *= g;if(n != -1) if(int(f.size()) > n) f.resize(n + 1);pq.push(f);}P res = pq.top();res.resize(n + 1);return res;}};using fps = FormalPowerSeries<mint>;int main(){int n, m;cin >> n >> m;vector<int> a(n);cin >> a;string s;cin >> s;vector<int> cnt(2 * m + 1);cnt[m] = -1;int shift = m;int sum = -1;for(int i = 0; i < m; i++){if(s[i] == 's'){shift--;cnt[shift] = -1 - sum;sum = -1;}if(s[i] == 'a'){cnt[shift]--;sum--;}}Merge<FormalPowerSeries<mint>> p(n), q(n);rep(i, m + 1){if(cnt[shift + i] > 0){rep(j, abs(cnt[shift + i])){fps tmp = {1, -(1 + i)};p.push(tmp);}}if(cnt[shift + i] < 0){rep(j, abs(cnt[shift + i])){fps tmp = {1, -(1 + i)};q.push(tmp);}}}auto c = (p.get() * q.get().inv(n)).pre(n);mint ans = 0;for(int k = 1; k <= n; k++) ans += a[k - 1] * c[k - 1] * c[n - k];// cout << c;cout << ans << "\n";return 0;}