#include #ifdef _MSC_VER # include #else # include #endif #include #include namespace suisen { // ! utility template using constraints_t = std::enable_if_t, std::nullptr_t>; template constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) { if constexpr (cond_v) { return std::forward(then); } else { return std::forward(or_else); } } // ! function template using is_same_as_invoke_result = std::is_same, ReturnType>; template using is_uni_op = is_same_as_invoke_result; template using is_bin_op = is_same_as_invoke_result; template using is_comparator = std::is_same, bool>; // ! integral template >> constexpr int bit_num = std::numeric_limits>::digits; template struct is_nbit { static constexpr bool value = bit_num == n; }; template static constexpr bool is_nbit_v = is_nbit::value; // ? template struct safely_multipliable {}; template <> struct safely_multipliable { using type = long long; }; template <> struct safely_multipliable { using type = __int128_t; }; template <> struct safely_multipliable { using type = unsigned long long; }; template <> struct safely_multipliable { using type = __uint128_t; }; template <> struct safely_multipliable { using type = __uint128_t; }; template <> struct safely_multipliable { using type = float; }; template <> struct safely_multipliable { using type = double; }; template <> struct safely_multipliable { using type = long double; }; template using safely_multipliable_t = typename safely_multipliable::type; template struct rec_value_type { using type = T; }; template struct rec_value_type> { using type = typename rec_value_type::type; }; template using rec_value_type_t = typename rec_value_type::type; } // namespace suisen // ! type aliases using i128 = __int128_t; using u128 = __uint128_t; template using pq_greater = std::priority_queue, std::greater>; // ! macros (internal) #define DETAIL_OVERLOAD2(_1,_2,name,...) name #define DETAIL_OVERLOAD3(_1,_2,_3,name,...) name #define DETAIL_OVERLOAD4(_1,_2,_3,_4,name,...) name #define DETAIL_REP4(i,l,r,s) for(std::remove_reference_t>i=(l);i<(r);i+=(s)) #define DETAIL_REP3(i,l,r) DETAIL_REP4(i,l,r,1) #define DETAIL_REP2(i,n) DETAIL_REP3(i,0,n) #define DETAIL_REPINF3(i,l,s) for(std::remove_reference_t>i=(l);;i+=(s)) #define DETAIL_REPINF2(i,l) DETAIL_REPINF3(i,l,1) #define DETAIL_REPINF1(i) DETAIL_REPINF2(i,0) #define DETAIL_RREP4(i,l,r,s) for(std::remove_reference_t>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s)) #define DETAIL_RREP3(i,l,r) DETAIL_RREP4(i,l,r,1) #define DETAIL_RREP2(i,n) DETAIL_RREP3(i,0,n) #define DETAIL_CAT_I(a, b) a##b #define DETAIL_CAT(a, b) DETAIL_CAT_I(a, b) #define DETAIL_UNIQVAR(tag) DETAIL_CAT(tag, __LINE__) // ! macros #define REP(...) DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_REP4 , DETAIL_REP3 , DETAIL_REP2 )(__VA_ARGS__) #define RREP(...) DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_RREP4 , DETAIL_RREP3 , DETAIL_RREP2 )(__VA_ARGS__) #define REPINF(...) DETAIL_OVERLOAD3(__VA_ARGS__, DETAIL_REPINF3, DETAIL_REPINF2, DETAIL_REPINF1)(__VA_ARGS__) #define LOOP(n) for (std::remove_reference_t> DETAIL_UNIQVAR(loop_variable) = n; DETAIL_UNIQVAR(loop_variable) --> 0;) #define ALL(iterable) std::begin(iterable), std::end(iterable) #define INPUT(type, ...) type __VA_ARGS__; read(__VA_ARGS__) // ! debug #ifdef LOCAL # define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__) template void debug_internal(const char* s, T&& first, Args&&... args) { constexpr const char* prefix = "[\033[32mDEBUG\033[m] "; constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "("; constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")"; std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward(first); ((std::cerr << ", " << std::forward(args)), ...); std::cerr << close_brakets << "\n"; } #else # define debug(...) void(0) #endif // ! I/O utilities // __int128_t std::ostream& operator<<(std::ostream& dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char* d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } // __uint128_t std::ostream& operator<<(std::ostream& dest, __uint128_t value) { std::ostream::sentry s(dest); if (s) { char buffer[128]; char* d = std::end(buffer); do { --d; *d = "0123456789"[value % 10]; value /= 10; } while (value != 0); int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } // pair template std::ostream& operator<<(std::ostream& out, const std::pair& a) { return out << a.first << ' ' << a.second; } // tuple template std::ostream& operator<<(std::ostream& out, const std::tuple& a) { if constexpr (N >= std::tuple_size_v>) return out; else { out << std::get(a); if constexpr (N + 1 < std::tuple_size_v>) out << ' '; return operator<<(out, a); } } // vector template std::ostream& operator<<(std::ostream& out, const std::vector& a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } // array template std::ostream& operator<<(std::ostream& out, const std::array& a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } inline void print() { std::cout << '\n'; } template inline void print(const Head& head, const Tail &...tails) { std::cout << head; if (sizeof...(tails)) std::cout << ' '; print(tails...); } template auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) { for (auto it = v.begin(); it != v.end();) { std::cout << *it; if (++it != v.end()) std::cout << sep; } std::cout << end; } __int128_t stoi128(const std::string& s) { __int128_t ret = 0; for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; if (s[0] == '-') ret = -ret; return ret; } __uint128_t stou128(const std::string& s) { __uint128_t ret = 0; for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; return ret; } // __int128_t std::istream& operator>>(std::istream& in, __int128_t& v) { std::string s; in >> s; v = stoi128(s); return in; } // __uint128_t std::istream& operator>>(std::istream& in, __uint128_t& v) { std::string s; in >> s; v = stou128(s); return in; } // pair template std::istream& operator>>(std::istream& in, std::pair& a) { return in >> a.first >> a.second; } // tuple template std::istream& operator>>(std::istream& in, std::tuple& a) { if constexpr (N >= std::tuple_size_v>) return in; else return operator>>(in >> std::get(a), a); } // vector template std::istream& operator>>(std::istream& in, std::vector& a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } // array template std::istream& operator>>(std::istream& in, std::array& a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } template void read(Args &...args) { (std::cin >> ... >> args); } // ! integral utilities // Returns pow(-1, n) template constexpr inline int pow_m1(T n) { return -(n & 1) | 1; } // Returns pow(-1, n) template <> constexpr inline int pow_m1(bool n) { return -int(n) | 1; } // Returns floor(x / y) template constexpr inline T fld(const T x, const T y) { return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y; } template constexpr inline T cld(const T x, const T y) { return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y; } template >, std::nullptr_t> = nullptr> __attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); } template , std::nullptr_t> = nullptr> __attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); } template >, std::nullptr_t> = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template , std::nullptr_t> = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num; } template >, std::nullptr_t> = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template , std::nullptr_t> = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num; } template constexpr inline int floor_log2(const T x) { return suisen::bit_num - 1 - count_lz(x); } template constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); } template constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; } template constexpr inline int parity(const T x) { return popcount(x) & 1; } // ! container template auto priqueue_comp(const Comparator comparator) { return std::priority_queue, Comparator>(comparator); } template void sort_unique_erase(Container& a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) { if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr); } template auto foreach_adjacent_values(Container &&c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) { foreach_adjacent_values(c.begin(), c.end(), f); } // ! other utilities // x <- min(x, y). returns true iff `x` has chenged. template inline bool chmin(T& x, const T& y) { return y >= x ? false : (x = y, true); } // x <- max(x, y). returns true iff `x` has chenged. template inline bool chmax(T& x, const T& y) { return y <= x ? false : (x = y, true); } template , std::nullptr_t> = nullptr> std::string bin(T val, int bit_num = -1) { std::string res; if (bit_num != -1) { for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1); } else { for (; val; val >>= 1) res += '0' + (val & 1); std::reverse(res.begin(), res.end()); } return res; } template , std::nullptr_t> = nullptr> std::vector digits_low_to_high(T val, T base = 10) { std::vector res; for (; val; val /= base) res.push_back(val % base); if (res.empty()) res.push_back(T{ 0 }); return res; } template , std::nullptr_t> = nullptr> std::vector digits_high_to_low(T val, T base = 10) { auto res = digits_low_to_high(val, base); std::reverse(res.begin(), res.end()); return res; } template std::string join(const std::vector& v, const std::string& sep, const std::string& end) { std::ostringstream ss; for (auto it = v.begin(); it != v.end();) { ss << *it; if (++it != v.end()) ss << sep; } ss << end; return ss.str(); } template auto transform_to_vector(const Func &f, const Seq &s) { std::vector> v; v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f); return v; } template auto copy_to_vector(const Seq &s) { std::vector v; v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v)); return v; } template Seq concat(Seq s, const Seq &t) { s.reserve(std::size(s) + std::size(t)); std::copy(std::begin(t), std::end(t), std::back_inserter(s)); return s; } template std::vector split(const Seq s, typename Seq::value_type delim) { std::vector res; for (auto itl = std::begin(s), itr = itl;; itl = ++itr) { while (itr != std::end(s) and *itr != delim) ++itr; res.emplace_back(itl, itr); if (itr == std::end(s)) return res; } } int digit_to_int(char c) { return c - '0'; } int lowercase_to_int(char c) { return c - 'a'; } int uppercase_to_int(char c) { return c - 'A'; } std::vector digit_str_to_ints(const std::string &s) { return transform_to_vector(digit_to_int, s); } std::vector lowercase_str_to_ints(const std::string &s) { return transform_to_vector(lowercase_to_int, s); } std::vector uppercase_str_to_ints(const std::string &s) { return transform_to_vector(uppercase_to_int, s); } template , std::enable_if_t< std::conjunction_v< std::is_invocable, std::is_invocable_r, std::invoke_result_t > >, std::nullptr_t> = nullptr > auto comparator(const ToKey &to_key, const CompareValue &compare_value = std::less<>()) { return [to_key, compare_value](const T& x, const T& y) { return compare_value(to_key(x), to_key(y)); }; } template , std::nullptr_t> = nullptr> std::vector sorted_indices(int n, const ToKey &to_key) { std::vector p(n); std::iota(p.begin(), p.end(), 0); std::sort(p.begin(), p.end(), comparator(to_key)); return p; } template , std::nullptr_t> = nullptr> std::vector sorted_indices(int n, const Compare &compare) { std::vector p(n); std::iota(p.begin(), p.end(), 0); std::sort(p.begin(), p.end(), compare); return p; } const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO"; namespace suisen {} using namespace suisen; using namespace std; struct io_setup { io_setup(int precision = 20) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(precision); } } io_setup_ {}; // ! code from here #include using mint = atcoder::modint1000000007; namespace atcoder { std::istream& operator>>(std::istream& in, mint &a) { long long e; in >> e; a = e; return in; } std::ostream& operator<<(std::ostream& out, const mint &a) { out << a.val(); return out; } } // namespace atcoder int main() { auto normalize = [](array &c) { vector vs; for (auto &e : c) if (e != -1) { vs.push_back(e); } sort_unique_erase(vs); for (auto &e : c) if (e != -1) { e = lower_bound(ALL(vs), e) - vs.begin(); } sort(ALL(c)); }; long long n; int k; read(k, n); map>, mint> memo; auto dfs = [&](auto dfs, int k, array c) -> mint { normalize(c); int cnum = *max_element(ALL(c)) + 1; if (k == 0) { return n - cnum; } pair key { k, c }; if (auto it = memo.find(key); it != memo.end()) { return it->second; } mint res = 0; for (int x = 0; x < cnum; ++x) { mint res01 = dfs(dfs, k - 1, array{ c[0], c[1], x }); mint res12 = dfs(dfs, k - 1, array{ c[1], c[2], x }); mint res20 = dfs(dfs, k - 1, array{ c[2], c[0], x }); res += res01 * res12 * res20; } mint res01 = dfs(dfs, k - 1, array{ c[0], c[1], cnum }); mint res12 = dfs(dfs, k - 1, array{ c[1], c[2], cnum }); mint res20 = dfs(dfs, k - 1, array{ c[2], c[0], cnum }); res += (n - cnum) * res01 * res12 * res20; return memo[{ k, c }] = res; }; print(dfs(dfs, k, { -1, -1, -1 })); }