#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 using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } MDCONST ModInt() : val_(0) {} MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } MDCONST explicit operator bool() const { return val_ != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val_); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val_ + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val_ % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv().val() % md); } MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; } MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; } MDCONST bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } MDCONST ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST ModInt inv() const { if (this->val_ < std::min(md >> 1, 1 << 21)) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } MDCONST ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } MDCONST ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } MDCONST ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template std::vector> ModInt::facs = {1}; template std::vector> ModInt::facinvs = {1}; template std::vector> ModInt::invs = {0}; using mint = ModInt<998244353>; // Integer convolution for arbitrary mod // with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class. // We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`. // input: a (size: n), b (size: m) // return: vector (size: n + m - 1) template std::vector nttconv(std::vector a, std::vector b, bool skip_garner); constexpr int nttprimes[3] = {998244353, 167772161, 469762049}; // Integer FFT (Fast Fourier Transform) for ModInt class // (Also known as Number Theoretic Transform, NTT) // is_inverse: inverse transform // ** Input size must be 2^n ** template void ntt(std::vector &a, bool is_inverse = false) { int n = a.size(); if (n == 1) return; static const int mod = MODINT::mod(); static const MODINT root = MODINT::get_primitive_root(); assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0); static std::vector w{1}, iw{1}; for (int m = w.size(); m < n / 2; m *= 2) { MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw; w.resize(m * 2), iw.resize(m * 2); for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv; } if (!is_inverse) { for (int m = n; m >>= 1;) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m] * w[k]; a[i] = x + y, a[i + m] = x - y; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m]; a[i] = x + y, a[i + m] = (x - y) * iw[k]; } } } int n_inv = MODINT(n).inv().val(); for (auto &v : a) v *= n_inv; } } template std::vector> nttconv_(const std::vector &a, const std::vector &b) { int sz = a.size(); assert(a.size() == b.size() and __builtin_popcount(sz) == 1); std::vector> ap(sz), bp(sz); for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i]; ntt(ap, false); if (a == b) bp = ap; else ntt(bp, false); for (int i = 0; i < sz; i++) ap[i] *= bp[i]; ntt(ap, true); return ap; } long long garner_ntt_(int r0, int r1, int r2, int mod) { using mint2 = ModInt; static const long long m01 = 1LL * nttprimes[0] * nttprimes[1]; static const long long m0_inv_m1 = ModInt(nttprimes[0]).inv().val(); static const long long m01_inv_m2 = mint2(m01).inv().val(); int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1]; auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2; return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod; } template std::vector nttconv(std::vector a, std::vector b, bool skip_garner) { if (a.empty() or b.empty()) return {}; int sz = 1, n = a.size(), m = b.size(); while (sz < n + m) sz <<= 1; if (sz <= 16) { std::vector ret(n + m - 1); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j]; } return ret; } int mod = MODINT::mod(); if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) { a.resize(sz), b.resize(sz); if (a == b) { ntt(a, false); b = a; } else { ntt(a, false), ntt(b, false); } for (int i = 0; i < sz; i++) a[i] *= b[i]; ntt(a, true); a.resize(n + m - 1); } else { std::vector ai(sz), bi(sz); for (int i = 0; i < n; i++) ai[i] = a[i].val(); for (int i = 0; i < m; i++) bi[i] = b[i].val(); auto ntt0 = nttconv_(ai, bi); auto ntt1 = nttconv_(ai, bi); auto ntt2 = nttconv_(ai, bi); a.resize(n + m - 1); for (int i = 0; i < n + m - 1; i++) a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod); } return a; } template std::vector nttconv(const std::vector &a, const std::vector &b) { return nttconv(a, b, false); } uint32_t rand_int() // XorShift random integer generator { static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123; uint32_t t = x ^ (x << 11); x = y; y = z; z = w; return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); } double rand_double() { return (double)rand_int() / UINT32_MAX; } #include #include #include #include int op(int l, int r) { return std::min(l, r); } int e() { return 0; } string solve(const string &S1, const string &S2) { const int N = S1.size(), M = S2.size(); string S1a = S1; for (auto &c : S1a) { if (c == '?') c = 'a'; } const auto z_algo = atcoder::z_algorithm(S2 + "_" + S1a); const auto sa = atcoder::suffix_array(S2 + "_" + S1a); vector sainv(sa.size()); REP(i, sa.size()) sainv.at(sa.at(i)) = i; const auto lcp = atcoder::lcp_array(S2 + "_" + S1a, sa); atcoder::segtree lcptree(lcp); REP(_, 1000) rand_int(); vector hash(26); for (auto &x : hash) x = rand_int(); vector f, g; for (auto c : S1) { if (c == '?') { f.push_back(0); } else { f.push_back(hash.at(c - 'a')); } } for (auto c : S2) g.push_back(hash.at(c - 'a')); auto f2 = f; for (auto &x : f2) x *= x; auto f3 = f2; REP(i, f3.size()) f3.at(i) *= f.at(i); auto g2 = g; for (auto &x : g2) x *= x; decltype(g) g0(g.size(), 1); reverse(ALL(g0)); reverse(ALL(g)); reverse(ALL(g2)); auto conv = nttconv(g0, f3), c2 = nttconv(g, f2), c3 = nttconv(g2, f); REP(i, conv.size()) conv.at(i) += c3.at(i) - c2.at(i) * 2; // dbg(conv); vector heads; FOR(i, M - 1, N) if (conv.at(i) == 0) heads.push_back(i - (M - 1)); dbg(heads); if (heads.empty()) return "-1"; // -1: same auto solve = [&](int l, int r) -> int { assert(l < r); if (r - l < M) { if (int z = z_algo.at(M + 1 + l); z < r - l) { auto rhs = S1a.at(l + z), lhs = S2.at(z); return lhs < rhs; } if (int z = z_algo.at(r - l); z < M - (r - l)) { auto lhs = S2.at(r - l + z), rhs = S2.at(r - l); return lhs < rhs; } int lcur = sainv.at(M + 1 + l + M), rcur = sainv.at(M - (r - l)); int matchlen = lcptree.prod(min(lcur, rcur), max(lcur, rcur)); if (matchlen >= r - l) return -1; auto lhs = S1a.at(l + M + matchlen), rhs = S2.at(M - (r - l) + matchlen); return lhs < rhs; } else { int lcur = sainv.at(0), rcur = sainv.at(M + 1 + l); int match = lcptree.prod(min(lcur, rcur), max(lcur, rcur)); if (match < M) { auto lhs = S2.at(match); auto rhs = S1a.at(l + match); return lhs < rhs; } lcur = sainv.at(M + 1 + r), rcur = sainv.at(0); match = lcptree.prod(min(lcur, rcur), max(lcur, rcur)); if (match < M) { auto lhs = S2.at(r + match); auto rhs = S1a.at(match); return lhs < rhs; } return -1; } }; auto comp = [&](int l, int r) -> bool { if (l == r) return false; if (l < r) { auto ret = solve(l, r); if (ret < 0) return false; return ret; } else { auto ret = solve(r, l); if (ret < 0) return false; return ret ^ 1; } }; std::sort(heads.begin(), heads.end(), comp); string ret = S1a.substr(0, heads.front()) + S2 + S1a.substr(heads.front() + S2.size()); return ret; } int main() { int T; cin >> T; while (T--) { int N, M; string S1, S2; cin >> N >> M >> S1 >> S2; cout << solve(S1, S2) << '\n'; } }