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MACRO_OUT(__VA_ARGS__); #define FOUT(n, dist) scan_out<=(a);--w) #define RREP(w, n) RFOR(w, 0, n) template bool IN(S a, T x, U b) { return a <= x && x < b; } template inline bool CHMAX(T& a, const T b) { if (a < b) { a = b; return true; } return false; } template inline bool CHMIN(T& a, const T b) { if (a > b) { a = b; return true; } return false; } // test template using V = std::vector; template using VV = V>; // //std::ostream& operator<<(std::ostream& os, const __int128& t) { // if (t >= 1000000000000000000) { // os << (long long)(t / 1000000000000000000) << (long long)(t % 1000000000000000000); // } // else { // os << (long long)t; // } // return os; //} template std::ostream& operator<<(std::ostream& os, const std::pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { os << '{'; for (size_t i = 0; i < v.size(); ++i) os << v[i] << ((i + 1 < v.size()) ? ',' : '}'); return os; } template std::ostream& operator<<(std::ostream& os, const std::set& v) { os << '{'; for (auto it = v.cbegin(); it != v.cend();) { os << *it << (++it == v.cend() ? '}' : ','); } return os; } template std::ostream& operator<<(std::ostream& os, const std::map& m) { os << '{'; for (auto it = m.cbegin(); it != m.cend();) { os << it->first << ':' << it->second; ++it; os << (it != m.cend() ? ',' : '}'); } return os; } template std::ostream& operator<<(std::ostream& os, std::queue q) { os << '<'; while (!q.empty()) { os << q.front(); q.pop(); os << (q.empty() ? '<' : ','); } return os; } template std::ostream& operator<<(std::ostream& os, std::stack q) { os << '>'; while (!q.empty()) { os << q.top(); q.pop(); os << (q.empty() ? ']' : ','); } return os; } namespace std { template class numeric_limits> { public: static constexpr pair max() noexcept { return { numeric_limits::max(), numeric_limits::max() }; } static constexpr pair lowest() noexcept { return { numeric_limits::lowest(), numeric_limits::lowest() }; } }; } // type/const using i64 = long long; using u64 = unsigned long long; using ll = long long; using ull = unsigned long long; using ld = long double; using PAIR = std::pair; constexpr int INFINT = (1 << 30) - 1; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr long long INFLL = 1LL << 60; // 1.15x10^18 constexpr long long INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18 constexpr double EPS = 1e-12; constexpr int MOD = 998244353; constexpr double PI = 3.141592653589793238462643383279; template void FILL(T(&a)[N], const T& val) { for (auto& x : a) x = val; } template void FILL(ARY(&a)[N][M], const T& val) { for (auto& b : a) FILL(b, val); } template void FILL(std::vector& a, const T& val) { for (auto& x : a) x = val; } template void FILL(std::vector>& a, const T& val) { for (auto& b : a) FILL(b, val); } // ------------>8------------------------>8------------ class ModInt { friend std::istream& operator>>(std::istream& is, ModInt& obj); private: inline ModInt& normUpper() { if (val >= MOD) val -= MOD; return *this; } inline ModInt& normLower() { if (val < 0) val += MOD; return *this; } inline ModInt& norm() { return normUpper(), normLower(); } public: constexpr static int numOfPrecalc = 1000006; static ModInt inv[numOfPrecalc]; int val; ModInt() : val(0) {} ModInt(int n) : val(n) { if (n >= MOD || n <= -MOD) n %= MOD; norm(); } ModInt(long long n) : ModInt((int)(n% MOD)) {} ModInt& operator=(const ModInt& r) { val = r.val; return *this; } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt(MOD - val); } ModInt& operator+=(const ModInt& r) { val += r.val; return normUpper(); } ModInt& operator-=(const ModInt& r) { val -= r.val; return normLower(); } ModInt& operator*=(const ModInt& r) { val = (long long)val * r.val % MOD; return *this; } ModInt& operator/=(ModInt r) { return *this *= (r.val < numOfPrecalc) ? inv[r.val] : (r ^= MOD - 2); } ModInt& operator^=(int p) { ModInt t(*this); *this = 1; for (; p; p >>= 1, t *= t) if (p & 1) *this *= t; return *this; } const ModInt operator+(const ModInt& r) const { return ModInt(*this) += r; } const ModInt operator-(const ModInt& r) const { return ModInt(*this) -= r; } const ModInt operator*(const ModInt& r) const { return ModInt(*this) *= r; } const ModInt operator/(const ModInt& r) const { return ModInt(*this) /= r; } const ModInt operator^(int p) const { return ModInt(*this) ^= p; } }; const ModInt operator+(long long l, const ModInt& r) { return ModInt(l) += r; } const ModInt operator-(long long l, const ModInt& r) { return ModInt(l) -= r; } const ModInt operator*(long long l, const ModInt& r) { return ModInt(l) *= r; } const ModInt operator/(long long l, const ModInt& r) { return ModInt(l) /= r; } const ModInt operator+(int l, const ModInt& r) { return ModInt(l) += r; } const ModInt operator-(int l, const ModInt& r) { return ModInt(l) -= r; } const ModInt operator*(int l, const ModInt& r) { return ModInt(l) *= r; } const ModInt operator/(int l, const ModInt& r) { return ModInt(l) /= r; } std::ostream& operator<<(std::ostream& os, const ModInt& obj) { return os << obj.val; } /* friend */ std::istream& operator>>(std::istream& is, ModInt& obj) { is >> obj.val; obj.norm(); return is; } ModInt ModInt::inv[ModInt::numOfPrecalc]; struct Init_ModInt { Init_ModInt() { ModInt::inv[1] = 1; for (int i = 2; i < ModInt::numOfPrecalc; ++i) ModInt::inv[i] = (MOD - MOD / i) * ModInt::inv[MOD % i]; } } _init_modint; /** ModInt **/ enum NodeType { fMAX, fMEX, fM_X, val, SIZE }; struct Node { Node* l, * r; NodeType type; ModInt dp[3]; }; Node* expr(std::string::iterator& it) { Node* node = new Node(); REP(i, 3) node->dp[i] = 0; while (*it != '$' && *it != ',' && *it != ')') { if (*it == 'm') { ++it; if (*it == 'a') { node->type = fMAX; } else if (*it == 'e') { node->type = fMEX; } else { // ? node->type = fM_X; } ++it; // x ++it; // ( ++it; node->l = expr(it); // , ++it; node->r = expr(it); // ) ++it; break; } else if (std::isdigit(*it)) { node->dp[*it - '0'] = 1; node->type = val; ++it; break; } else { // ? REP(i, 3) node->dp[i] = 1; node->type = val; ++it; } } return node; } int mex(int i, int j) { int p = 0; while (i == p || j == p) ++p; return p; } signed main() { INIT; VAR(std::string, s); VAR(int, k); s += '$'; auto it = s.begin(); Node* root = expr(it); auto rec = [&](auto&& f, Node* r) -> void { if (r->type != val) { f(f, r->l); f(f, r->r); if (r->type == fMAX) { REP(i, 3) REP(j, 3) { r->dp[std::max(i, j)] += r->l->dp[i] * r->r->dp[j]; } } else if (r->type == fMEX) { REP(i, 3) REP(j, 3) { r->dp[mex(i, j)] += r->l->dp[i] * r->r->dp[j]; } } else if (r->type == fM_X) { REP(i, 3) REP(j, 3) { r->dp[std::max(i, j)] += r->l->dp[i] * r->r->dp[j]; r->dp[mex(i, j)] += r->l->dp[i] * r->r->dp[j]; } } } }; rec(rec, root); EOUT(root->dp[k]); return 0; }