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 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,491 ms / 4,000 ms |
| コード長 | 33,524 bytes |
| コンパイル時間 | 3,924 ms |
| コンパイル使用メモリ | 243,772 KB |
| 実行使用メモリ | 75,812 KB |
| 最終ジャッジ日時 | 2024-06-12 07:44:52 |
| 合計ジャッジ時間 | 42,402 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 6 ms
6,940 KB |
| testcase_02 | AC | 36 ms
6,940 KB |
| testcase_03 | AC | 672 ms
6,944 KB |
| testcase_04 | AC | 23 ms
6,940 KB |
| testcase_05 | AC | 58 ms
6,940 KB |
| testcase_06 | AC | 78 ms
6,940 KB |
| testcase_07 | AC | 3 ms
6,944 KB |
| testcase_08 | AC | 18 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | AC | 17 ms
6,944 KB |
| testcase_11 | AC | 1,491 ms
60,892 KB |
| testcase_12 | AC | 1,251 ms
75,688 KB |
| testcase_13 | AC | 1,251 ms
75,812 KB |
| testcase_14 | AC | 1,183 ms
53,160 KB |
| testcase_15 | AC | 1,483 ms
60,896 KB |
| testcase_16 | AC | 1,206 ms
6,940 KB |
| testcase_17 | AC | 1,270 ms
9,524 KB |
| testcase_18 | AC | 1,168 ms
53,208 KB |
| testcase_19 | AC | 1,166 ms
53,204 KB |
| testcase_20 | AC | 1,180 ms
53,204 KB |
| testcase_21 | AC | 1,177 ms
53,072 KB |
| testcase_22 | AC | 1,171 ms
53,192 KB |
| testcase_23 | AC | 1,176 ms
53,120 KB |
| testcase_24 | AC | 1,170 ms
53,216 KB |
| testcase_25 | AC | 1,178 ms
53,200 KB |
| testcase_26 | AC | 1,187 ms
53,200 KB |
| testcase_27 | AC | 1,180 ms
53,204 KB |
| testcase_28 | AC | 1,193 ms
53,072 KB |
| testcase_29 | AC | 1,213 ms
60,856 KB |
| testcase_30 | AC | 1,211 ms
60,960 KB |
| testcase_31 | AC | 1,205 ms
60,852 KB |
| testcase_32 | AC | 1,204 ms
60,980 KB |
| testcase_33 | AC | 1,198 ms
60,740 KB |
| testcase_34 | AC | 1,196 ms
60,900 KB |
| testcase_35 | AC | 1,199 ms
60,800 KB |
| testcase_36 | AC | 1,220 ms
60,980 KB |
| testcase_37 | AC | 1,214 ms
60,896 KB |
| testcase_38 | AC | 1,215 ms
60,852 KB |
| testcase_39 | AC | 554 ms
9,728 KB |
| testcase_40 | AC | 375 ms
8,940 KB |
| testcase_41 | AC | 2 ms
6,940 KB |
| testcase_42 | AC | 2 ms
6,944 KB |
| testcase_43 | AC | 2 ms
6,940 KB |
| testcase_44 | AC | 122 ms
6,940 KB |
ソースコード
#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();
}