/** * date : 2024-12-12 23:46:05 * author : Nyaan */ using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template using minpq = priority_queue, greater>; template struct P : pair { template constexpr P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(T &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template vector> product(const vector &a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I, const function &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function{[](T &) -> void {}}); } template T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector &v) { using U = typename T::value_type; if (v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template vector Rotate(const vector &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return __builtin_popcountll(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #endif #ifndef NyaanDebug #define trc(...) (void(0)) #endif #ifndef NyaanLocal #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto &&x : v) #define each2(x, y, v) for (auto &&[x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N) - 1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b) - 1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // using namespace std; template vector z_algorithm(const Container &s) { int n = s.size(); if (n == 0) return {}; vector a(n); a[0] = n; int i = 1, j = 0; while (i < n) { while (i + j < n && s[j] == s[i + j]) j++; a[i] = j; if (j == 0) { i++; continue; } int k = 1; while (i + k < n && k + a[k] < j) a[i + k] = a[k], k++; i += k, j -= k; } return a; } /** * @brief Z algorithm */ // (p, l, r) : S[l, r) は周期 p かつ極大 // sum_{(p,l,r)} 1 <= n // sum_{(p,l,r)} (r-l)/p <= 3n // sum_{(p,l,r)} (r-l+1-2*p) = O(n log n) template vector> run_enumerate(const C &S) { int N = S.size(); using T = tuple; vector>> by_p(N + 1); auto solve_sub = [&](const C &l, const C &r) { vector res; int n = l.size(), m = r.size(); C s = l, t = r; t.insert(end(t), begin(l), end(l)); t.insert(end(t), begin(r), end(r)); reverse(begin(s), end(s)); auto ZS = z_algorithm(s), ZT = z_algorithm(t); for (int p = 1; p <= n; p++) { int a = p == n ? p : min(ZS[p] + p, n); int b = min(ZT[n + m - p], m); if (a + b < 2 * p) continue; res.emplace_back(p, a, b); } return res; }; auto dfs = [&](auto rc, int L, int R) -> void { if (R - L <= 1) return; int M = (L + R) / 2; rc(rc, L, M), rc(rc, M, R); C SL{begin(S) + L, begin(S) + M}; C SR{begin(S) + M, begin(S) + R}; auto sub_res1 = solve_sub(SL, SR); for (auto &[p, a, b] : sub_res1) by_p[p].emplace_back(M - a, M + b); reverse(begin(SL), end(SL)); reverse(begin(SR), end(SR)); auto sub_res2 = solve_sub(SR, SL); for (auto &[p, a, b] : sub_res2) by_p[p].emplace_back(M - b, M + a); }; dfs(dfs, 0, N); vector res; set> done; for (int p = 0; p <= N; p++) { auto &LR = by_p[p]; sort(begin(LR), end(LR), [](auto &x, auto &y) { if (x.first == y.first) return x.second > y.second; return x.first < y.first; }); int r = -1; for (auto &lr : LR) { if (r >= lr.second) continue; r = lr.second; if (!done.count(lr)) { done.insert(lr); res.emplace_back(p, lr.first, lr.second); } } } return res; } using namespace Nyaan; constexpr int INF = 1001001001; template struct SWAG { vector a0, a1, r0, r1; T f0, f1; T f(const T &a, const T &b) { return a.first < b.first ? a : b; } static constexpr T I{INF, -1}; SWAG() : f0(I), f1(I) {} private: void push_s0(const T &x) { a0.push_back(x); r0.push_back(f0 = f(x, f0)); } void push_s1(const T &x) { a1.push_back(x); r1.push_back(f1 = f(f1, x)); } void transfer() { while (!a1.empty()) { push_s0(a1.back()); a1.pop_back(); } while (!r1.empty()) r1.pop_back(); f1 = I; } public: void push(const T &x) { if (a0.empty()) { push_s0(x); transfer(); } else { push_s1(x); } } T pop() { if (a0.empty()) transfer(); T res = a0.back(); a0.pop_back(); r0.pop_back(); f0 = r0.empty() ? I : r0.back(); return res; } T query() { return f(f0, f1); } int size() { return a0.size() + a1.size(); } }; struct Data { vector>> dat; static constexpr int size_table[9] = { 9, 90, 900, 9000, 90000, 900000, 9000000, 90000000, 900000000, }; Data() { dat.push_back({}); } void push(int val, int pos) { dat[0].push({val, pos}); for (int i = 0; i < (int)dat.size(); i++) { if ((int)dat[i].size() <= size_table[i]) break; if (i + 1 == (int)dat.size()) dat.push_back({}); dat[i + 1].push(dat[i].pop()); } } pair query() { int res = INF, pos = -1; for (int i = 0; i < (int)dat.size(); i++) { auto [val, idx] = dat[i].query(); val += i + 1; if (val < res) res = val, pos = idx; } return {res, pos}; } }; int min_period(string S) { int N = sz(S); vi z = z_algorithm(S); rep1(i, N - 1) { if (N % i != 0) continue; if (z[i] == N - i) return i; } return N; } int num_len(int x) { return to_string(x).size(); } string naive(string S) { int N = sz(S); vector dp(N + 1, inf); vector prev(N + 1, -1); dp[0] = 0; rep(i, N) reg(j, i + 1, N + 1) { int p = min_period(S.substr(i, j - i)); int val = dp[i] + p + num_len((j - i) / p); if (amin(dp[j], val)) prev[j] = i; } string ans; for (int j = N; j != 0;) { int i = prev[j]; int p = min_period(S.substr(i, j - i)); string cur = S.substr(i, p) + to_string((j - i) / p); reverse(all(cur)); ans += cur; j = i; } reverse(all(ans)); assert(sz(ans) == dp[N]); return ans; } string calc(string S) { int N = sz(S); auto run = run_enumerate(S); VV rundata(N + 1); for (auto &[p, l, r] : run) { rep(i, p) { if (l + i + 2 * p <= r) rundata[l + i + 2 * p].emplace_back(r, p); else break; } } vector dp(N + 1, inf); vector prev(N + 1, -1); dp[0] = 0; // dp[i] - i を保持する int prev_best = inf, prev_pos = -1; struct Data2 { int p, r; Data dat; }; VV datas(N + 1); rep(i, N + 1) { // dp[j] (j 15) return {}; string sub = T.substr(i, j - i); int num = stoll(T.substr(j, k - j)); while (num--) { res += sub; if ((int)res.size() > limit) return res; } i = k; } return res; } void check(string S) { auto an = naive(S); auto ac = calc(S); assert(restore(an, sz(S)) == S); assert(restore(ac, sz(S)) == S); if (sz(an) != sz(ac)) { trc2(S, an, ac); exit(1); } } void q() { /* check("baaaaaaaaa"); check("aabababc"); check("aaaaaaaaaa"); rep1(len, 11) { rep(b, Power(3, len)) { string S; for (int x = b; sz(S) < len; x /= 3) S.push_back(x % 3 + 'a'); check(S); } trc2(len, "OK"); } rep1(len, 18) { rep(b, PW(len)) { string S; rep(i, len) S.push_back('a' + gbit(b, i)); check(S); } trc2(len, "OK"); } */ ins(S); auto ans = calc(S); assert(restore(ans, sz(S)) == S); out(ans); } void Nyaan::solve() { int t = 1; in(t); while (t--) q(); }