#include #define REP_(i, a_, b_, a, b, ...) \ for (int i = (a), END_##i = (b); i < END_##i; ++i) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define ALL(x) std::begin(x), std::end(x) using i64 = long long; #include using Mint = atcoder::modint998244353; std::ostream &operator<<(std::ostream &os, const Mint &m) { return os << m.val(); } template inline bool chmax(T &a, U b) { return a < b and ((a = std::move(b)), true); } template inline bool chmin(T &a, U b) { return a > b and ((a = std::move(b)), true); } template inline int ssize(const T &a) { return (int) std::size(a); } template std::istream &operator>>(std::istream &is, std::vector &a) { for (auto &x: a) is >> x; return is; } template std::ostream &operator<<(std::ostream &os, const std::pair &a) { return os << "(" << a.first << ", " << a.second << ")"; } template std::ostream &print_seq(const Container &a, std::string_view sep = " ", std::string_view ends = "\n", std::ostream &os = std::cout) { auto b = std::begin(a), e = std::end(a); for (auto it = std::begin(a); it != e; ++it) { if (it != b) os << sep; os << *it; } return os << ends; } template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type { }; template::value && !std::is_same::value && !std::is_same::value>> std::ostream &operator<<(std::ostream &os, const T &a) { return print_seq(a, ", ", "", (os << "{")) << "}"; } void print() { std::cout << "\n"; } template void print(const T &x) { std::cout << x << "\n"; } template void print(const Head &head, Tail... tail) { std::cout << head << " "; print(tail...); } struct Input { template operator T() const { T x; std::cin >> x; return x; } } in; #ifdef MY_DEBUG #include "debug_dump.hpp" #else #define DUMP(...) #endif using namespace std; struct Node { bool max; bool mex; bool l0; bool l1; bool l2; array child; Node() : max(false), mex(false), l0(false), l1(false), l2(false), child{nullptr, nullptr} {} }; int mex(int x, int y) { if (x != 0 and y != 0) return 0; if (x != 1 and y != 1) return 1; return 2; } auto solve() -> Mint { const string s = in; const int K = in; const int n = s.size(); auto parse = [&](auto &f, int pos) -> pair { assert(pos < n); Node *t = new Node(); if (s[pos] == 'm') { assert(s[pos + 2] == 'x'); char mc = s[pos + 1]; if (mc == 'a') { t->max = true; } else if (mc == 'e') { t->mex = true; } else if (mc == '?') { t->max = t->mex = true; } else { assert(false); } assert(s[pos + 3] == '('); auto[c1, j1] = f(f, pos + 4); assert(s[j1] == ','); auto[c2, j2] = f(f, j1 + 1); assert(s[j2] == ')'); t->child[0] = c1; t->child[1] = c2; return {t, j2 + 1}; } if (s[pos] == '0') { t->l0 = true; } else if (s[pos] == '1') { t->l1 = true; } else if (s[pos] == '2') { t->l2 = true; } else if (s[pos] == '?') { t->l0 = t->l1 = t->l2 = true; } else { assert(false); } return {t, pos + 1}; }; auto[t, pos] = parse(parse, 0); assert(pos == n); /* auto ptree = [&](auto &f, Node *node, int d) -> void { REP(i, d) cerr << " "; if (node->max or node->mex) { cerr << "(a:" << node->max << ", e:" << node->mex << "\n"; f(f, node->child[0], d + 1); f(f, node->child[1], d + 1); REP(i, d) cerr << " "; cerr << ")\n"; } else { cerr << "(0:" << node->l0 << ", 1:" << node->l1 << ", 2:" << node->l2 << ")\n"; } }; ptree(ptree, t, 0); */ auto dfs = [&](auto &f, Node *node) -> array { array ret = {0, 0, 0}; if (node->max or node->mex) { auto r0 = f(f, node->child[0]); auto r1 = f(f, node->child[1]); if (node->max) { REP(i, 3) REP(j, 3) { ret[max(i, j)] += r0[i] * r1[j]; } } if (node->mex) { REP(i, 3) REP(j, 3) { ret[mex(i, j)] += r0[i] * r1[j]; } } } else { if (node->l0) ret[0]++; if (node->l1) ret[1]++; if (node->l2) ret[2]++; } return ret; }; auto res = dfs(dfs, t); DUMP(res); return res[K]; } int main() { ios_base::sync_with_stdio(false), cin.tie(nullptr); cout << std::fixed << std::setprecision(18); const int t = 1; REP(test_case, t) { auto ans = solve(); print(ans); } }