#line 1 "yukicoder\\b.cpp" #include #line 5 "Library\\config.hpp" namespace config { const auto start_time{std::chrono::system_clock::now()}; int64_t elapsed() { using namespace std::chrono; const auto end_time{system_clock::now()}; return duration_cast(end_time - start_time).count(); } __attribute__((constructor)) void setup() { using namespace std; ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); #ifdef _buffer_check atexit([] { char bufc; if (cin >> bufc) cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n"; }); #endif } unsigned cases(void), caseid = 1; template void main() { for (const unsigned total = cases(); caseid <= total; ++caseid) C(); } } // namespace config #line 3 "Library\\gcc_builtin.hpp" namespace workspace { constexpr int clz32(const uint32_t &n) noexcept { return __builtin_clz(n); } constexpr int clz64(const uint64_t &n) noexcept{ return __builtin_clzll(n); } constexpr int ctz(const uint64_t &n) noexcept { return __builtin_ctzll(n); } constexpr int popcnt(const uint64_t &n) noexcept { return __builtin_popcountll(n); } } // namespace workspace #line 2 "Library\\gcc_option.hpp" #ifdef ONLINE_JUDGE #pragma GCC optimize("O3") #pragma GCC target("avx,avx2") #pragma GCC optimize("unroll-loops") #endif #line 5 "Library\\utils\\binary_search.hpp" namespace workspace { // binary search on discrete range. template std::enable_if_t< std::is_convertible_v, bool>, iter_type> binary_search(iter_type ok, iter_type ng, pred_type pred) { assert(ok != ng); __int128_t dist(ng - ok); while (dist > 1 || dist < -1) { iter_type mid(ok + dist / 2); if (pred(mid)) ok = mid, dist -= dist / 2; else ng = mid, dist /= 2; } return ok; } // parallel binary search on discrete range. template std::enable_if_t>, std::vector>, std::vector> binary_search(std::vector> ends, pred_type pred) { std::vector mids(ends.size()); for (;;) { bool all_found = true; for (size_t i{}; i != ends.size(); ++i) { auto [ok, ng] = ends[i]; iter_type mid(ok + (ng - ok) / 2); if (mids[i] != mid) { all_found = false; mids[i] = mid; } } if (all_found) break; auto res = pred(mids); for (size_t i{}; i != ends.size(); ++i) { (res[i] ? ends[i].first : ends[i].second) = mids[i]; } } return mids; } // binary search on real numbers. template std::enable_if_t< std::is_convertible_v, bool>, real_type> binary_search(real_type ok, real_type ng, const real_type eps, pred_type pred) { assert(ok != ng); while (ok + eps < ng || ng + eps < ok) { real_type mid{(ok + ng) / 2}; (pred(mid) ? ok : ng) = mid; } return ok; } // parallel binary search on real numbers. template std::enable_if_t>, std::vector>, std::vector> binary_search(std::vector> ends, const real_type eps, pred_type pred) { std::vector mids(ends.size()); for (;;) { bool all_found = true; for (size_t i{}; i != ends.size(); ++i) { auto [ok, ng] = ends[i]; if (ok + eps < ng || ng + eps < ok) { all_found = false; mids[i] = (ok + ng) / 2; } } if (all_found) break; auto res = pred(mids); for (size_t i{}; i != ends.size(); ++i) { (res[i] ? ends[i].first : ends[i].second) = mids[i]; } } return mids; } } // namespace workspace #line 3 "Library\\utils\\casefmt.hpp" namespace workspace { std::ostream &casefmt(std::ostream& os) { return os << "Case #" << config::caseid << ": "; } } // namespace workspace #line 3 "Library\\utils\\chval.hpp" namespace workspace { template > bool chle(T &x, const T &y, Comp comp = Comp()) { return comp(y, x) ? x = y, true : false; } template > bool chge(T &x, const T &y, Comp comp = Comp()) { return comp(x, y) ? x = y, true : false; } } // namespace workspace #line 3 "Library\\utils\\fixed_point.hpp" namespace workspace { // specify the return type of lambda. template class fixed_point { lambda_type func; public: fixed_point(lambda_type &&f) : func(std::move(f)) {} template auto operator()(Args &&... args) const { return func(*this, std::forward(args)...); } }; } // namespace workspace #line 3 "Library\\utils\\sfinae.hpp" #include template class trait> using enable_if_trait_type = typename std::enable_if::value>::type; template using element_type = typename std::decay()))>::type; template struct is_integral_ext : std::false_type {}; template struct is_integral_ext< T, typename std::enable_if::value>::type> : std::true_type {}; template <> struct is_integral_ext<__int128_t> : std::true_type {}; template <> struct is_integral_ext<__uint128_t> : std::true_type {}; template constexpr static bool is_integral_ext_v = is_integral_ext::value; template struct multiplicable_uint { using type = uint_least32_t; }; template struct multiplicable_uint::type> { using type = uint_least64_t; }; template struct multiplicable_uint::type> { using type = __uint128_t; }; #line 7 "Library\\utils\\hash.hpp" namespace workspace { template struct hash : std::hash {}; template struct hash> { size_t operator()(uint64_t x) const { static const uint64_t m = std::random_device{}(); x ^= x >> 23; // x *= 0x2127599bf4325c37ULL; x ^= m; x ^= x >> 47; return x - (x >> 32); } }; template size_t hash_combine(const size_t &seed, const Key &key) { return seed ^ (hash()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */ ); } template struct hash> { size_t operator()(const std::pair &pair) const { return hash_combine(hash()(pair.first), pair.second); } }; template class hash> { template ::value - 1> struct tuple_hash { static uint64_t apply(const Tuple &t) { return hash_combine(tuple_hash::apply(t), std::get(t)); } }; template struct tuple_hash { static uint64_t apply(const Tuple &t) { return 0; } }; public: uint64_t operator()(const std::tuple &t) const { return tuple_hash>::apply(t); } }; template struct hash_table_wrapper : hash_table { using key_type = typename hash_table::key_type; size_t count(const key_type &key) const { return hash_table::find(key) != hash_table::end(); } template auto emplace(Args&&... args) { return hash_table::insert(typename hash_table::value_type(args...)); } }; template using cc_hash_table = hash_table_wrapper<__gnu_pbds::cc_hash_table>>; template using gp_hash_table = hash_table_wrapper<__gnu_pbds::gp_hash_table>>; template using unordered_map = std::unordered_map>; template using unordered_set = std::unordered_set>; } // namespace workspace #line 3 "Library\\utils\\make_vector.hpp" namespace workspace { template constexpr auto make_vector(size_t* sizes, T const& init = T()) { if constexpr (N) return std::vector(*sizes, make_vector(std::next(sizes), init)); else return init; } template constexpr auto make_vector(const size_t (&sizes)[N], T const& init = T()) { return make_vector((size_t*)sizes, init); } } // namespace workspace #line 3 "Library\\utils\\read.hpp" namespace workspace { // read with std::cin. template struct read { typename std::remove_const::type value; template read(types... args) : value(args...) { std::cin >> value; } operator T() const { return value; } }; template <> struct read { template operator T() const { T value; std::cin >> value; return value; } }; } // namespace workspace #line 4 "Library\\utils\\stream.hpp" #line 6 "Library\\utils\\stream.hpp" namespace std { template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tuple_is { static istream &apply(istream &is, tuple_t &t) { tuple_is::apply(is, t); return is >> get(t); } }; template struct tuple_is { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tuple_is, tuple_size>::value - 1>::apply(is, t); } template struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { tuple_os::apply(os, t); return os << ' ' << get(t); } }; template struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { return os; } }; template ostream &operator<<(ostream &os, const tuple &t) { return tuple_os, tuple_size>::value - 1>::apply(os, t); } template > typename enable_if::type, string>::value && !is_same::type, char *>::value, istream &>::type operator>>(istream &is, Container &cont) { for (auto &&e : cont) is >> e; return is; } template > typename enable_if::type, string>::value && !is_same::type, char *>::value, ostream &>::type operator<<(ostream &os, const Container &cont) { bool head = true; for (auto &&e : cont) head ? head = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #line 14 "yukicoder\\b.cpp" namespace workspace { constexpr char eol = '\n'; using namespace std; using i64 = int_least64_t; using p32 = pair; using p64 = pair; template > using priority_queue = std::priority_queue, Comp>; template using stack = std::stack>; struct solver; } // namespace workspace int main() { config::main(); } unsigned config::cases() { // return -1; // not specify // int t; std::cin >> t; return t; // given return 1; } #line 4 "Library\\modulus\\modint.hpp" #line 6 "Library\\modulus\\modint.hpp" template struct modint { static_assert(is_integral_ext::value, "Mod must be integral type."); static_assert(!(Mod < 0), "Mod must be non-negative."); using mod_type = typename std::conditional< Mod != 0, typename std::add_const::type, Mod_type>::type; static mod_type mod; using value_type = typename std::decay::type; constexpr operator value_type() const noexcept { return value; } constexpr static modint one() noexcept { return 1; } constexpr modint() noexcept = default; template ::value>::type * = nullptr> constexpr modint(int_type n) noexcept : value((n %= mod) < 0 ? mod + n : n) {} constexpr modint(bool n) noexcept : modint(int(n)) {} constexpr modint operator++(int) noexcept { modint t{*this}; return operator+=(1), t; } constexpr modint operator--(int) noexcept { modint t{*this}; return operator-=(1), t; } constexpr modint &operator++() noexcept { return operator+=(1); } constexpr modint &operator--() noexcept { return operator-=(1); } constexpr modint operator-() const noexcept { return value ? mod - value : 0; } constexpr modint &operator+=(const modint &rhs) noexcept { return (value += rhs.value) < mod ? 0 : value -= mod, *this; } constexpr modint &operator-=(const modint &rhs) noexcept { return (value += mod - rhs.value) < mod ? 0 : value -= mod, *this; } constexpr modint &operator*=(const modint &rhs) noexcept { return value = (typename multiplicable_uint::type)value * rhs.value % mod, *this; } constexpr modint &operator/=(const modint &rhs) noexcept { return operator*=(rhs.inverse()); } template constexpr typename std::enable_if::value, modint>::type operator+(const int_type &rhs) const noexcept { return modint{*this} += rhs; } constexpr modint operator+(const modint &rhs) const noexcept { return modint{*this} += rhs; } template constexpr typename std::enable_if::value, modint>::type operator-(const int_type &rhs) const noexcept { return modint{*this} -= rhs; } constexpr modint operator-(const modint &rhs) const noexcept { return modint{*this} -= rhs; } template constexpr typename std::enable_if::value, modint>::type operator*(const int_type &rhs) const noexcept { return modint{*this} *= rhs; } constexpr modint operator*(const modint &rhs) const noexcept { return modint{*this} *= rhs; } template constexpr typename std::enable_if::value, modint>::type operator/(const int_type &rhs) const noexcept { return modint{*this} /= rhs; } constexpr modint operator/(const modint &rhs) const noexcept { return modint{*this} /= rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator+(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) + rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator-(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) - rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator*(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) * rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator/(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) / rhs; } constexpr modint inverse() const noexcept { assert(value); value_type a{mod}, b{value}, u{}, v{1}, t{}; while (b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } template constexpr typename std::enable_if::value, modint>::type power(int_type e) noexcept { if (e < 0) e = e % (mod - 1) + mod - 1; modint res{1}, p{*this}; for (modint p{value}; e; e >>= 1, p *= p) { if (e & 1) res *= p; } return res; } friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.value; } friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { intmax_t value; rhs = (is >> value, value); return is; } protected: value_type value = 0; }; template typename modint::mod_type modint::mod = Mod; using modint_runtime = modint<0>; #line 33 "yukicoder\\b.cpp" struct workspace::solver { using mint = modint<1000000007>; solver() { // start here! int n; cin >> n; int c; cin >> c; vector> tr(n); for (int i = 1; i < n; i++) { int a, b; cin >> a >> b; --a, --b; tr[a].emplace_back(b); tr[b].emplace_back(a); } using table = unordered_map; auto dp = fixed_point([&](auto dfs, int now, int pre) -> table { bool is_root = !~pre; if (!is_root) tr[now].erase(find(begin(tr[now]), end(tr[now]), pre)); table dp; for (int i = 1; i <= c and i <= n * 6; i++) dp[i] = 1; for (int i = 0, j = c; i < 6 * n and j > 0; j--, i++) dp[j] = 1; for (int to : tr[now]) { auto cdp = dfs(to, now); int i; for (i = 1; i < 6 * n and i <= c; i++) dp[i] *= cdp[i - 3] + cdp[i + 3]; for (int j = c; j >= i and c - j < 6 * n; j--) dp[j] *= cdp[j - 3] + cdp[j + 3]; } return dp; })(0, -1); // answer mint ans; { int k, l; for (k = 1; k <= c && k <= n * 3; k++) { ans += dp[k]; } for (l = c; l > k && l > c - n * 3; l--) { ans += dp[l]; } ans += max(0, l - k + 1) * dp[n * 3]; } cout << ans << eol; } };