結果

問題 No.2231 Surprising Flash!
ユーザー gyouzasushi
提出日時 2023-02-27 06:29:13
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,571 ms / 4,000 ms
コード長 33,524 bytes
コンパイル時間 3,849 ms
コンパイル使用メモリ 236,744 KB
最終ジャッジ日時 2025-02-10 23:52:51
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 1
other AC * 44
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ソースコード

diff #
プレゼンテーションモードにする

#line 1 "main.cpp"
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())
using namespace std;
using ll = long long;
const int INF = 1e9;
const ll LINF = 1e18;
template <class T>
void get_unique(vector<T>& x) {
    x.erase(unique(x.begin(), x.end()), x.end());
}
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
vector<T> make_vec(size_t a) {
    return vector<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        is >> v[i];
    }
    return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        os << v[i];
        if (i < sz(v) - 1) os << ' ';
    }
    return os;
}
#line 3 "/Users/gyouzasushi/kyopro/library/math/convolution.hpp"
#include <type_traits>
#line 5 "/Users/gyouzasushi/kyopro/library/math/convolution.hpp"
#line 2 "/Users/gyouzasushi/kyopro/library/math/modint.hpp"
#line 5 "/Users/gyouzasushi/kyopro/library/math/modint.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}
}  // namespace internal
#line 35 "/Users/gyouzasushi/kyopro/library/math/modint.hpp"
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}
// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;
    // @param m `1 <= m`
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {
    }
    // @return m
    unsigned int umod() const {
        return _m;
    }
    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay
        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1)
        // < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (long long a : {2, 7, 61}) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b
        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
}  // namespace internal
#line 214 "/Users/gyouzasushi/kyopro/library/math/modint.hpp"
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
                              unsigned __int128>;
template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
#else
template <class T>
using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using to_unsigned =
    typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
}  // namespace internal
#line 299 "/Users/gyouzasushi/kyopro/library/math/modint.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
}  // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;
public:
    static constexpr int mod() {
        return m;
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    static_modint() : _v(0) {
    }
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) {
        _v = ((unsigned int)(v) % umod());
    }
    unsigned int val() const {
        return _v;
    }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) {
        return *this = *this * rhs.inv();
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
private:
    unsigned int _v;
    static constexpr unsigned int umod() {
        return m;
    }
    static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;
public:
    static int mod() {
        return (int)(bt.umod());
    }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    dynamic_modint() : _v(0) {
    }
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) {
        _v = ((unsigned int)(v) % mod());
    }
    unsigned int val() const {
        return _v;
    }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) {
        return *this = *this * rhs.inv();
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() {
        return bt.umod();
    }
};
template <int id>
internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
}  // namespace internal
#line 599 "/Users/gyouzasushi/kyopro/library/math/modint.hpp"
template <typename T, typename std::enable_if_t<internal::is_modint<T>::value,
                                                std::nullptr_t> = nullptr>
std::istream& operator>>(std::istream& is, T& v) {
    long long x;
    is >> x;
    v = x;
    return is;
}
template <typename T, typename std::enable_if_t<internal::is_modint<T>::value,
                                                std::nullptr_t> = nullptr>
std::ostream& operator<<(std::ostream& os, const T& v) {
    os << v.val();
    return os;
}
#line 7 "/Users/gyouzasushi/kyopro/library/math/convolution.hpp"
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = internal::bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[internal::bsf(~(unsigned int)(s))];
        }
    }
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = internal::bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }
    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                    inow.val();
            }
            inow *= sum_ie[internal::bsf(~(unsigned int)(s))];
        }
    }
}
}  // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) {
        if (n < m) {
            std::swap(n, m);
            std::swap(a, b);
        }
        std::vector<mint> ans(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
        return ans;
    }
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}
template <unsigned int mod = 998244353, class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;
    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);
    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
    return c;
}
#line 54 "main.cpp"
vector<ll> f(vector<ll> a, vector<ll> b) {
    reverse(all(b));
    vector c = convolution_ll(a, b);
    return vector(c.begin() + sz(b) - 1, c.end());
}
// ret[i] := s[i..i+m] と t がマッチするか
vector<bool> match(string s, string t) {
    int n = sz(s), m = sz(t);
    vector<ll> a1(n), a2(n), a3(n);
    rep(i, n) {
        a1[i] = s[i] == '?' ? 0 : ll(s[i]);
        a2[i] = a1[i] * a1[i];
        a3[i] = a2[i] * a1[i];
    }
    vector<ll> b1(m), b2(m), b3(m);
    rep(i, m) {
        b1[i] = t[i] == '?' ? 0 : ll(t[i]);
        b2[i] = b1[i] * b1[i];
        b3[i] = b2[i] * b1[i];
    }
    vector c1 = f(a3, b1);
    vector c2 = f(a2, b2);
    vector c3 = f(a1, b3);
    vector<bool> ret(n);
    rep(i, n) {
        ret[i] = c1[i] - c2[i] * 2 + c3[i] == 0;
    }
    return ret;
}
#line 7 "/Users/gyouzasushi/kyopro/library/string/rolling_hash.hpp"
#line 3 "/Users/gyouzasushi/kyopro/library/math/modint2305843009213693951.hpp"
struct modint2305843009213693951 {
    using mint = modint2305843009213693951;
public:
    static constexpr uint64_t mod = 2305843009213693951;
    modint2305843009213693951() : _v(0) {
    }
    modint2305843009213693951(uint64_t v) : _v(fast_mod(v)) {
    }
    static constexpr uint64_t fast_mod(uint64_t v) {
        uint64_t u = v >> 61;
        uint64_t d = v & mod;
        uint64_t x = u + d;
        if (x > mod) x -= mod;
        return x;
    }
    uint64_t val() const {
        return _v;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= mod) _v -= mod;
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= mod) _v += mod;
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        static constexpr uint64_t mask31 = (uint64_t(1) << 31) - 1;
        static constexpr uint64_t mask30 = (uint64_t(1) << 30) - 1;
        uint64_t au = _v >> 31;
        uint64_t ad = _v & mask31;
        uint64_t bu = rhs._v >> 31;
        uint64_t bd = rhs._v & mask31;
        uint64_t m = ad * bu + au * bd;
        uint64_t mu = m >> 30;
        uint64_t md = m & mask30;
        _v = fast_mod((au * bu << 1) + mu + (md << 31) + ad * bd);
        return *this;
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
    mint pow(uint64_t n) const {
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
private:
    uint64_t _v;
};
#line 3 "/Users/gyouzasushi/kyopro/library/math/pow_table.hpp"
template <typename mint>
struct pow_mods {
    pow_mods() {
    }
    pow_mods(mint base, int n) : base(base) {
        ensure(n);
    }
    const mint& operator[](int i) const {
        ensure(i);
        return pows[i];
    }
    void ensure(int n) const {
        int sz = pows.size();
        if (sz > n) return;
        pows.resize(n + 1);
        for (int i = sz; i <= n; i++) pows[i] = base * pows[i - 1];
    }
private:
    mutable std::vector<mint> pows{1};
    mint base;
    static constexpr int mod = mint::mod;
};
#line 10 "/Users/gyouzasushi/kyopro/library/string/rolling_hash.hpp"
template <int base_num = 1, typename mint = modint2305843009213693951>
struct RollingHash {
public:
    RollingHash() {
    }
    RollingHash(const std::vector<int>& a) : n(a.size()) {
        for (int base_id = 0; base_id < base_num; base_id++) {
            hashes[base_id].resize(n + 1);
            hashes[base_id][0] = 0;
            for (int i = 0; i < n; i++) {
                hashes[base_id][i + 1] =
                    hashes[base_id][i] * bases[base_id] + a[i];
            }
        }
    }
    template <typename Iterable>
    static RollingHash from(const Iterable& s) {
        std::vector<int> a;
        for (auto&& e : s) a.push_back(int(e));
        return RollingHash(a);
    }
    std::array<mint, base_num> operator()(int l, int r) {
        assert(0 <= l && l <= r && r <= n);
        std::array<mint, base_num> res;
        for (int base_id = 0; base_id < base_num; base_id++) {
            res[base_id] =
                hashes[base_id][r] - hashes[base_id][l] * pows[base_id][r - l];
        }
        return res;
    }
    static std::array<mint, base_num> concat(
        const std::array<mint, base_num>& h1,
        const std::array<mint, base_num>& h2, int h2_len) {
        std::array<mint, base_num> res;
        for (int base_id = 0; base_id < base_num; base_id++) {
            res[base_id] = h1[base_id] * pows[base_id][h2_len] + h2[base_id];
        }
        return res;
    }
    int lcp(int l1, int r1, int l2, int r2) {
        int len = std::min(r1 - l1, r2 - l2);
        int ok = 0, ng = len + 1;
        while (ng - ok > 1) {
            int mid = (ok + ng) / 2;
            bool f = (*this)(l1, l1 + mid) == (*this)(l2, l2 + mid);
            (f ? ok : ng) = mid;
        }
        return ok;
    }
    int cmp(int l1, int r1, int l2, int r2) {
        int x = std::min({lcp(l1, r1, l2, r2), r1 - l1, r2 - l2});
        if (l1 + x == r1 && l2 + x != r2) return -1;
        if (l1 + x == r1 && l2 + x == r2) return 0;
        if (l1 + x != r1 && l2 + x == r2) return 1;
        return (*this)(l1 + x, l1 + x + 1)[0].val() <
                       (*this)(l2 + x, l2 + x + 1)[0].val()
                   ? -1
                   : 1;
    }
    static int lcp(RollingHash<base_num, mint>& rh1, int l1, int r1,
                   RollingHash<base_num, mint>& rh2, int l2, int r2) {
        int len = std::min(r1 - l1, r2 - l2);
        int ok = 0, ng = len + 1;
        while (ng - ok > 1) {
            int mid = (ok + ng) / 2;
            bool f = rh1(l1, l1 + mid) == rh2(l2, l2 + mid);
            (f ? ok : ng) = mid;
        }
        return ok;
    }
    static int cmp(RollingHash<base_num, mint>& rh1, int l1, int r1,
                   RollingHash<base_num, mint>& rh2, int l2, int r2) {
        int x = std::min({lcp(rh1, l1, r1, rh2, l2, r2), r1 - l1, r2 - l2});
        if (l1 + x == r1 && l2 + x != r2) return -1;
        if (l1 + x == r1 && l2 + x == r2) return 0;
        if (l1 + x != r1 && l2 + x == r2) return 1;
        return rh1(l1 + x, l1 + x + 1)[0].val() <
                       rh2(l2 + x, l2 + x + 1)[0].val()
                   ? -1
                   : 1;
    }
private:
    static inline std::array<mint, base_num> gen_bases() {
        static std::mt19937_64 rng(std::random_device{}());
        std::array<mint, base_num> bases;
        for (int i = 0; i < base_num; i++) {
            while (true) {
                uint64_t k = std::uniform_int_distribution<uint64_t>(
                    1, mint::mod - 1)(rng);
                if (std::gcd(k, mint::mod - 1) != 1) continue;
                uint64_t b = mint(r).pow(k).val();
                if (b <= A) continue;
                bases[i] = b;
                break;
            }
        }
        return bases;
    }
    static inline std::array<pow_mods<mint>, base_num> init_pows(
        const std::array<mint, base_num>& bases) {
        std::array<pow_mods<mint>, base_num> pows;
        for (int i = 0; i < base_num; i++) {
            pows[i] = pow_mods<mint>(bases[i], 0);
        }
        return pows;
    }
    static inline std::array<mint, base_num> bases = gen_bases();
    static inline std::array<pow_mods<mint>, base_num> pows = init_pows(bases);
    int n;
    std::array<std::vector<mint>, base_num> hashes;
    static constexpr uint64_t r = 37;
    static constexpr uint64_t A = 2147483647;
};
#line 84 "main.cpp"
void solve() {
    int n, m;
    cin >> n >> m;
    string s, t;
    cin >> s >> t;
    vector ok = match(s, t);
    rep(i, n) if (s[i] == '?') s[i] = 'a';
    auto rhs = RollingHash<>::from(s);
    auto rht = RollingHash<>::from(t);
    auto gt = [&](int i, int j) {
        if (i > j) swap(i, j);
        if (i == -1) return true;
        if (j - i > m) {
            int cmp1 = RollingHash<>::cmp(rht, 0, m, rhs, i, i + m);
            if (cmp1 != 0) return cmp1 == 1;
            int cmp2 = RollingHash<>::cmp(rhs, j, j + m, rht, 0, m);
            return cmp2 == 1;
        }
        int cmp1 = RollingHash<>::cmp(rht, 0, j - i, rhs, i, j);
        if (cmp1 != 0) return cmp1 == 1;
        int cmp2 = rht.cmp(j - i, m, 0, m - (j - i));
        if (cmp2 != 0) return cmp2 == 1;
        int cmp3 = RollingHash<>::cmp(rhs, i + m, j + m, rht, m - (j - i), m);
        return cmp3 == 1;
    };
    int ans = -1;
    rep(i, n - m + 1) if (ok[i]) {
        if (gt(ans, i)) ans = i;
    }
    cerr << ans << '\n';
    if (ans == -1) {
        cout << -1 << '\n';
        return;
    }
    rep(i, m) s[ans + i] = t[i];
    cout << s << '\n';
    return;
}
int main() {
    int tt;
    cin >> tt;
    while (tt--) solve();
}
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