#ifdef ONLINE_JUDGE #include #include #else #include #endif using ll = long long; using lll = __int128_t; #define rep(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i) #define reps(i, n) for (int i = 1, i##_len = (n); i <= i##_len; ++i) #define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i) #define rreps(i, n) for (int i = ((int)(n)); i > 0; --i) #define rep2(i, s, n) for (int i = (s); i < (int)(n); i++) #define repc2(i, s, n) for (int i = (s); i <= (int)(n); i++) #define length(v) ((int)(v).size()) constexpr int inf = 2'000'000'000; constexpr ll linf = 4'000'000'000'000'000'000, M7 = 1'000'000'007, M9 = 998'244'353; #define all(v) begin(v), end(v) #define rall(v) rbegin(v), rend(v) using namespace std; using namespace atcoder; // clang-format off #define Vec(type, ...) __make_vec(__VA_ARGS__) template vector __make_vec(size_t a) {return vector(a);}template auto __make_vec(size_t a, Ts... ts) {return vector(ts...))>(a, __make_vec(ts...));} #define VecI(init, type, ...) __make_vecI(__VA_ARGS__) template vector __make_vecI(size_t a) {return vector(a, init);} template auto __make_vecI(size_t a, Ts... ts) {return vector(ts...))>(a, __make_vecI(ts...));} template inline ostream& operator<<(ostream& os, const pair& p) noexcept {return os << p.first << " " << p.second;} inline ostream& operator<<(ostream& os, const modint& m) noexcept { return os << m.val(); } template inline ostream& operator<<(ostream& os, const static_modint& m) noexcept { return os << m.val(); } template struct is_static_modint : std::false_type {}; template struct is_static_modint> : std::true_type {}; template