#include #include using namespace std; using ll = long long int; using u64 = unsigned long long; using pll = pair; // #include // using namespace atcoder; #define REP(i, a, b) for (ll i = (a); i < (b); i++) #define REPrev(i, a, b) for (ll i = (a); i >= (b); i--) #define ALL(coll) (coll).begin(), (coll).end() #define SIZE(v) ((ll)((v).size())) #define REPOUT(i, a, b, exp, sep) REP(i, (a), (b)) cout << (exp) << (i + 1 == (b) ? "" : (sep)); cout << "\n" // @@ !! LIM(debug) // ---- inserted function f:<< from util.cc // declarations template ostream& operator<< (ostream& os, const pair& p); template ostream& operator<< (ostream& os, const tuple& t); template ostream& operator<< (ostream& os, const tuple& t); template ostream& operator<< (ostream& os, const tuple& t); template ostream& operator<< (ostream& os, const tuple& t); template ostream& operator<< (ostream& os, const vector& v); template ostream& operator<< (ostream& os, const set& v); template ostream& operator<< (ostream& os, const unordered_set& v); template ostream& operator<< (ostream& os, const multiset& v); template ostream& operator<< (ostream& os, const map& mp); template ostream& operator<< (ostream& os, const unordered_map& mp); template ostream& operator<< (ostream& os, const queue& orig); template ostream& operator<< (ostream& os, const deque& orig); template ostream& operator<< (ostream& os, const priority_queue& orig); template ostream& operator<< (ostream& os, const stack& st); #if __cplusplus >= 201703L template ostream& operator<< (ostream& os, const optional& t); #endif ostream& operator<< (ostream& os, int8_t x); ostream& operator<< (ostream& os, const __int128& x); // definitions template ostream& operator<< (ostream& os, const pair& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } template ostream& operator<< (ostream& os, const tuple& t) { os << "(" << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << ")"; return os; } template ostream& operator<< (ostream& os, const tuple& t) { os << "(" << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << ", " << get<3>(t) << ")"; return os; } template ostream& operator<< (ostream& os, const tuple& t) { os << "(" << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << ", " << get<3>(t) << ", " << get<4>(t) << ")"; return os; } template ostream& operator<< (ostream& os, const tuple& t) { os << "(" << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << ", " << get<3>(t) << ", " << get<4>(t) << ", " << get<5>(t) << ")"; return os; } template ostream& operator<< (ostream& os, const vector& v) { os << '['; for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) os << ", "; os << *it; } os << ']'; return os; } template ostream& operator<< (ostream& os, const set& v) { os << '{'; for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) os << ", "; os << *it; } os << '}'; return os; } template ostream& operator<< (ostream& os, const unordered_set& v) { os << '{'; for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) os << ", "; os << *it; } os << '}'; return os; } template ostream& operator<< (ostream& os, const multiset& v) { os << '{'; for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) os << ", "; os << *it; } os << '}'; return os; } template ostream& operator<< (ostream& os, const map& mp) { os << '['; for (auto it = mp.begin(); it != mp.end(); it++) { if (it != mp.begin()) os << ", "; os << it->first << ": " << it->second; } os << ']'; return os; } template ostream& operator<< (ostream& os, const unordered_map& mp) { os << '['; for (auto it = mp.begin(); it != mp.end(); it++) { if (it != mp.begin()) os << ", "; os << it->first << ": " << it->second; } os << ']'; return os; } template ostream& operator<< (ostream& os, const queue& orig) { queue que(orig); bool first = true; os << '['; while (!que.empty()) { T x = que.front(); que.pop(); if (!first) os << ", "; os << x; first = false; } return os << ']'; } template ostream& operator<< (ostream& os, const deque& orig) { deque que(orig); bool first = true; os << '['; while (!que.empty()) { T x = que.front(); que.pop_front(); if (!first) os << ", "; os << x; first = false; } return os << ']'; } template ostream& operator<< (ostream& os, const priority_queue& orig) { priority_queue pq(orig); bool first = true; os << '['; while (!pq.empty()) { T x = pq.top(); pq.pop(); if (!first) os << ", "; os << x; first = false; } return os << ']'; } template ostream& operator<< (ostream& os, const stack& st) { stack tmp(st); os << '['; bool first = true; while (!tmp.empty()) { T& t = tmp.top(); if (first) first = false; else os << ", "; os << t; tmp.pop(); } os << ']'; return os; } #if __cplusplus >= 201703L template ostream& operator<< (ostream& os, const optional& t) { if (t.has_value()) os << "v(" << t.value() << ")"; else os << "nullopt"; return os; } #endif ostream& operator<< (ostream& os, int8_t x) { os << (int32_t)x; return os; } // for Enum type; just displays ordinals. template typename std::enable_if::value, std::ostream&>::type operator<<(std::ostream& os, E e) { return os << static_cast::type>(e); } // This is a very ad-hoc implementation... ostream& operator<<(ostream& os, const __int128& v) { unsigned __int128 a = v < 0 ? -v : v; ll i = 0; string s(64, ' '); if (v == 0) { s[i++] = '0'; }else { while (a > 0) { s[i++] = '0' + (char)(a % 10); a /= 10; } } if (v < 0) { s[i++] = '-'; } s.erase(s.begin() + i, s.end()); reverse(s.begin(), s.end()); os << s; return os; } // ---- end f:<< // ---- inserted library file debug.cc template string dbgFormat(const char* fmt, Args... args) { size_t len = snprintf(nullptr, 0, fmt, args...); char buf[len + 1]; snprintf(buf, len + 1, fmt, args...); return string(buf); } template void dbgLog(bool with_nl, Head&& head) { cerr << head; if (with_nl) cerr << endl; } template void dbgLog(bool with_nl, Head&& head, Tail&&... tail) { cerr << head << " "; dbgLog(with_nl, forward(tail)...); } #if DEBUG #define DLOG(...) dbgLog(true, __VA_ARGS__) #define DLOGNNL(...) dbgLog(false, __VA_ARGS__) #define DFMT(...) cerr << dbgFormat(__VA_ARGS__) << endl #define DCALL(func, ...) func(__VA_ARGS__) #else #define DLOG(...) #define DLOGNNL(...) #define DFMT(...) #define DCALL(func, ...) #endif /* #if DEBUG_LIB #define DLOG_LIB(...) dbgLog(true, __VA_ARGS__) #define DLOGNNL_LIB(...) dbgLog(false, __VA_ARGS__) #define DFMT_LIB(...) cerr << dbgFormat(__VA_ARGS__) << endl #define DCALL_LIB(func, ...) func(__VA_ARGS__) #else #define DLOG_LIB(...) #define DFMT_LIB(...) #define DCALL_LIB(func, ...) #endif */ #define DUP1(E1) #E1 "=", E1 #define DUP2(E1,E2) DUP1(E1), DUP1(E2) #define DUP3(E1,...) DUP1(E1), DUP2(__VA_ARGS__) #define DUP4(E1,...) DUP1(E1), DUP3(__VA_ARGS__) #define DUP5(E1,...) DUP1(E1), DUP4(__VA_ARGS__) #define DUP6(E1,...) DUP1(E1), DUP5(__VA_ARGS__) #define DUP7(E1,...) DUP1(E1), DUP6(__VA_ARGS__) #define DUP8(E1,...) DUP1(E1), DUP7(__VA_ARGS__) #define DUP9(E1,...) DUP1(E1), DUP8(__VA_ARGS__) #define DUP10(E1,...) DUP1(E1), DUP9(__VA_ARGS__) #define DUP11(E1,...) DUP1(E1), DUP10(__VA_ARGS__) #define DUP12(E1,...) DUP1(E1), DUP11(__VA_ARGS__) #define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,NAME,...) NAME #define DUP(...) GET_MACRO(__VA_ARGS__, DUP12, DUP11, DUP10, DUP9, DUP8, DUP7, DUP6, DUP5, DUP4, DUP3, DUP2, DUP1)(__VA_ARGS__) #define DLOGK(...) DLOG(DUP(__VA_ARGS__)) #define DLOGKL(lab, ...) DLOG(lab, DUP(__VA_ARGS__)) #if DEBUG_LIB #define DLOG_LIB DLOG #define DLOGK_LIB DLOGK #define DLOGKL_LIB DLOGKL #endif // ---- end debug.cc // @@ !! LIM -- end mark -- int main(/* int argc, char *argv[] */) { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << setprecision(20); vector power3(13); power3[0] = 1; REP(i, 1, 13) power3[i] = power3[i - 1] * 3; vector fact(4); fact[0] = 1; fact[1] = 1; fact[2] = 2; fact[3] = 6; vector tbl(8, vector(13, -1LL)); auto f = [&](auto rF, u64 x, ll len) -> ll { ll& r = tbl[x][len]; if (r < 0) { if (len == 0) { if (x == 0) r = 1; else r = 0; } else if (x == 0) r = power3[len]; else if (popcount(x) > len) r = 0; else if (popcount(x) == len) r = fact[len]; else { r = 0; r += rF(rF, x & ~(1LL), len - 1); r += rF(rF, x & ~(2LL), len - 1); r += rF(rF, x & ~(4LL), len - 1); } } return r; }; ll N; cin >> N; ll S; cin >> S; ll x = 7LL; string ans; REP(i, 0, N) { ll a = f(f, x & ~(1LL), N - i - 1); DLOGK(i, a, S); if (S <= a) { ans += 'A'; x &= ~(1LL); }else { S -= a; ll b = f(f, x & ~(2LL), N - i - 1); DLOGK(i, b, S); if (S <= b) { ans += 'B'; x &= ~(2LL); }else { S -= b; ll c = f(f, x & ~(4LL), N - i - 1); DLOGK(i, c, S); if (S <= c) { ans += 'C'; x &= ~(4LL); }else { cout << -1 << endl; return 0; } } } } cout << ans << endl; return 0; }