#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) (x1)*(y2)-(x2)*(y1) #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) (x1)*(y2)*(z3)+(x2)*(y3)*(z1)+(x3)*(y1)*(z2)-(z1)*(y2)*(x3)-(z2)*(y3)*(x1)-(z3)*(y1)*(x2) #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; using func = pair; val opm(val a, val b) { return min(a, b); } val em() { return 1e18; } val opM(val a, val b) { return max(a, b); } val eM() { return 0; } //val mp(func f, val a) //{ // if (f.first < 0) // return a; // return f; //} //func comp(func f, func g) { // if (g.first < 0) // return f; // return g; //} // //func id() { // return MP(-1, -1); //} ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; ll si[4] = { 0,3,3,0 }; ll sj[4] = { 0,0,3,3 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; void solve() { ll n; cin >> n; vector precalc = { "", "a", "ab", "aab", "aaba", "aabba", "aaabba", "aaababb", "aaababba", "aaababbaa", "aaababbbaa", "aaaababbbaa", "aaaabaabbbab", "aaaabaabbabbb", "aaaabaabbabbba", "aaaabaabbababbb", "aaaabaabbababbba", "aaaabaabbababbbaa", "aaaabaabbababbbaaa", "aaaabaabbababbbbaaa" }; if (n < precalc.size()) { cout << precalc[n] << "\n"; return; } vector> lfsr = { {}, {}, {0,1}, {0,1}, {0,1}, {0,2}, {0,1}, {0,1}, {0,2,3,4}, {0,4}, {0,3}, {0,2}, {0,1,2,8}, {0,1,2,5}, {0,1,2,12}, {0,1}, {0,2,3,5}, {0,3}, {0,7}, {0,1,2,5} }; ll lfsr_i = 2; while ((1 << (lfsr_i + 1)) + lfsr_i < n) { lfsr_i++; } ll vn = 1LL << (lfsr_i); VVL g(vn); ll first = vn >> 1; ll now = first; ll cnt = lfsr_i; ll top_bit = vn >> 1; while (now != 1) { ll next_bit = 0; for (auto& v : lfsr[lfsr_i]) next_bit ^= (now >> v) & 1; ll next = (now >> 1) | (next_bit * top_bit); g[now].push_back(next); now = next; cnt++; } g[now].push_back(0); cnt++; g[0].push_back(first); cnt++; REP(i, vn) { if (g[i].size() > 1) continue; VL add; ll now = i; while (cnt < n) { ll next = g[now][0] ^ top_bit; g[now].push_back(next); cnt++; add.push_back(now); now = next; if (now == i) break; } if (cnt == n) { string ans; for (auto& v : add) swap(g[v][0], g[v][1]); ll now = i; REP(b, lfsr_i) { if (EXISTBIT(now, b)) ans.push_back('B'); else ans.push_back('A'); } while (!g[now].empty()) { ll next = g[now].back(); if (next & top_bit) ans.push_back('B'); else ans.push_back('A'); g[now].pop_back(); now = next; } cout << ans << "\n"; return; } } return; } int main() { ll t = 1; cin >> t; while (t--) { solve(); } return 0; }