結果
| 問題 | No.2231 Surprising Flash! |
| ユーザー |
 nok0
|
| 提出日時 | 2023-02-24 23:00:19 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 743 ms / 4,000 ms |
| コード長 | 55,042 bytes |
| コンパイル時間 | 3,902 ms |
| コンパイル使用メモリ | 264,212 KB |
| 最終ジャッジ日時 | 2025-02-10 22:10:28 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 44 |
コンパイルメッセージ
/home/nok0/documents/programming/library/template/input.hpp: In function ‘void scanner::scan(char*)’: /home/nok0/documents/programming/library/template/input.hpp:29:33: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
ソースコード
#line 1 "/home/nok0/documents/programming/library/atcoder/convolution.hpp"
#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>
#line 1 "/home/nok0/documents/programming/library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
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`
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) 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
} // namespace atcoder
#line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
#line 5 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
#include <numeric>
#line 7 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
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 modular multiplication 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 < 2^31`
explicit 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;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
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);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"
#line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"
namespace atcoder {
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
} // namespace atcoder
#line 14 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
namespace atcoder {
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());
}
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());
}
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
} // namespace atcoder
#line 12 "/home/nok0/documents/programming/library/atcoder/convolution.hpp"
namespace atcoder {
namespace internal {
template <class mint,
int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 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()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
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;
}
} // 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) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
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;
}
} // namespace atcoder
#line 1 "/home/nok0/documents/programming/library/atcoder/string.hpp"
#line 7 "/home/nok0/documents/programming/library/atcoder/string.hpp"
#include <string>
#line 9 "/home/nok0/documents/programming/library/atcoder/string.hpp"
namespace atcoder {
namespace internal {
std::vector<int> sa_naive(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int l, int r) {
if (l == r) return false;
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] < s[r];
l++;
r++;
}
return l == n;
});
return sa;
}
std::vector<int> sa_doubling(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n), rnk = s, tmp(n);
std::iota(sa.begin(), sa.end(), 0);
for (int k = 1; k < n; k *= 2) {
auto cmp = [&](int x, int y) {
if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
int rx = x + k < n ? rnk[x + k] : -1;
int ry = y + k < n ? rnk[y + k] : -1;
return rx < ry;
};
std::sort(sa.begin(), sa.end(), cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
}
std::swap(tmp, rnk);
}
return sa;
}
// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
int n = int(s.size());
if (n == 0) return {};
if (n == 1) return {0};
if (n == 2) {
if (s[0] < s[1]) {
return {0, 1};
} else {
return {1, 0};
}
}
if (n < THRESHOLD_NAIVE) {
return sa_naive(s);
}
if (n < THRESHOLD_DOUBLING) {
return sa_doubling(s);
}
std::vector<int> sa(n);
std::vector<bool> ls(n);
for (int i = n - 2; i >= 0; i--) {
ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
}
std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
for (int i = 0; i < n; i++) {
if (!ls[i]) {
sum_s[s[i]]++;
} else {
sum_l[s[i] + 1]++;
}
}
for (int i = 0; i <= upper; i++) {
sum_s[i] += sum_l[i];
if (i < upper) sum_l[i + 1] += sum_s[i];
}
auto induce = [&](const std::vector<int>& lms) {
std::fill(sa.begin(), sa.end(), -1);
std::vector<int> buf(upper + 1);
std::copy(sum_s.begin(), sum_s.end(), buf.begin());
for (auto d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
std::vector<int> lms_map(n + 1, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms_map[i] = m++;
}
}
std::vector<int> lms;
lms.reserve(m);
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms.push_back(i);
}
}
induce(lms);
if (m) {
std::vector<int> sorted_lms;
sorted_lms.reserve(m);
for (int v : sa) {
if (lms_map[v] != -1) sorted_lms.push_back(v);
}
std::vector<int> rec_s(m);
int rec_upper = 0;
rec_s[lms_map[sorted_lms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sorted_lms[i - 1], r = sorted_lms[i];
int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
bool same = true;
if (end_l - l != end_r - r) {
same = false;
} else {
while (l < end_l) {
if (s[l] != s[r]) {
break;
}
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) rec_upper++;
rec_s[lms_map[sorted_lms[i]]] = rec_upper;
}
auto rec_sa =
sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
for (int i = 0; i < m; i++) {
sorted_lms[i] = lms[rec_sa[i]];
}
induce(sorted_lms);
}
return sa;
}
} // namespace internal
std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
assert(0 <= upper);
for (int d : s) {
assert(0 <= d && d <= upper);
}
auto sa = internal::sa_is(s, upper);
return sa;
}
template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
int n = int(s.size());
std::vector<int> idx(n);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
std::vector<int> s2(n);
int now = 0;
for (int i = 0; i < n; i++) {
if (i && s[idx[i - 1]] != s[idx[i]]) now++;
s2[idx[i]] = now;
}
return internal::sa_is(s2, now);
}
std::vector<int> suffix_array(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return internal::sa_is(s2, 255);
}
// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
const std::vector<int>& sa) {
int n = int(s.size());
assert(n >= 1);
std::vector<int> rnk(n);
for (int i = 0; i < n; i++) {
rnk[sa[i]] = i;
}
std::vector<int> lcp(n - 1);
int h = 0;
for (int i = 0; i < n; i++) {
if (h > 0) h--;
if (rnk[i] == 0) continue;
int j = sa[rnk[i] - 1];
for (; j + h < n && i + h < n; h++) {
if (s[j + h] != s[i + h]) break;
}
lcp[rnk[i] - 1] = h;
}
return lcp;
}
std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return lcp_array(s2, sa);
}
// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
int n = int(s.size());
if (n == 0) return {};
std::vector<int> z(n);
z[0] = 0;
for (int i = 1, j = 0; i < n; i++) {
int& k = z[i];
k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
std::vector<int> z_algorithm(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return z_algorithm(s2);
}
} // namespace atcoder
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"
const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"
namespace viewer {
void view(const long long &e) {
if(e == INF)
std::cerr << "INF";
else if(e == -INF)
std::cerr << "-INF";
else
std::cerr << e;
}
void view(const int &e) {
if(e == inf)
std::cerr << "inf";
else if(e == -inf)
std::cerr << "-inf";
else
std::cerr << e;
}
template <typename T>
void view(const T &e) {
std::cerr << e;
}
template <typename T, typename U>
void view(const std::pair<T, U> &p) {
std::cerr << "(";
view(p.first);
std::cerr << ", ";
view(p.second);
std::cerr << ")";
}
template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
std::cerr << "(";
view(std::get<0>(p));
std::cerr << ", ";
view(std::get<1>(p));
std::cerr << ", ";
view(std::get<2>(p));
std::cerr << ")";
}
template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
std::cerr << "(";
view(std::get<0>(p));
std::cerr << ", ";
view(std::get<1>(p));
std::cerr << ", ";
view(std::get<2>(p));
std::cerr << ", ";
view(std::get<3>(p));
std::cerr << ")";
}
template <typename T>
void view(const std::set<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::unordered_set<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::multiset<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::unordered_multiset<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::vector<T> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(const auto &e : v) {
view(e);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(const auto &e : v) {
view(e);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
std::cerr << "{\n";
for(const auto &v : vv) {
std::cerr << "\t";
view(v);
std::cerr << '\n';
}
std::cerr << "}";
}
template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
std::cerr << "{\n";
for(const auto &c : v) {
std::cerr << "\t(";
view(c.first);
std::cerr << ", ";
view(c.second);
std::cerr << ")\n";
}
std::cerr << "}";
}
template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << '{';
for(const auto &t : v) {
std::cerr << "\n\t";
view(t);
std::cerr << ",";
}
std::cerr << "\n}";
}
template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << '{';
for(const auto &t : v) {
std::cerr << "\n\t";
view(t);
std::cerr << ",";
}
std::cerr << "\n}";
}
template <typename T, typename U>
void view(const std::map<T, U> &m) {
std::cerr << "{\n";
for(const auto &t : m) {
std::cerr << "\t[";
view(t.first);
std::cerr << "] : ";
view(t.second);
std::cerr << '\n';
}
std::cerr << "}";
}
template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
std::cerr << "{\n";
for(const auto &t : m) {
std::cerr << "\t[";
view(t.first);
std::cerr << "] : ";
view(t.second);
std::cerr << '\n';
}
std::cerr << "}";
}
} // namespace viewer
// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
viewer::view(H);
std::cerr << ", ";
debug_out(T...);
}
#define debug(...) \
do { \
std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
debug_out(__VA_ARGS__); \
std::cerr << "\b\b]\n"; \
} while(0)
#define dump(x) \
do { \
std::cerr << __LINE__ << " " << #x << " : "; \
viewer::view(x); \
std::cerr << '\n'; \
} while(0)
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template<class T = int>
using V = std::vector<T>;
template<class T = int>
using VV = std::vector<std::vector<T>>;
template<class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"
struct fast_io {
fast_io() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(15);
}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"
template<class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &i : v) is >> i;
return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
std::string s;
is >> s;
__int128_t ret = 0;
for (int i = 0; i < (int)s.length(); i++)
if ('0' <= s[i] and s[i] <= '9')
ret = 10 * ret + s[i] - '0';
a = ret * (s[0] == '-' ? -1 : 1);
return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template<class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template<class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template<class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
scan(head);
INPUT(tail...);
}
} // namespace scanner
#define VEC(type, name, size) \
std::vector<type> name(size); \
scanner::INPUT(name)
#define VVEC(type, name, h, w) \
std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
scanner::INPUT(name)
#define INT(...) \
int __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define STR(...) \
std::string __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...) \
double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
T ret = 1;
while(n) {
if(n & 1) ret *= a;
a *= a;
n >>= 1;
}
return ret;
}
long long POW(long long a, long long n, const int mod) {
long long ret = 1;
a = (a % mod + mod) % mod;
while(n) {
if(n & 1) (ret *= a) %= mod;
(a *= a) %= mod;
n >>= 1;
}
return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
while(abs(ok - ng) > 1) {
T mid = (ok + ng) >> 1;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
for(int i = 0; i < loop; i++) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"
template<class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
for (int i = 0; i < int(a.size()); ++i) {
if (i) os << " ";
os << a[i];
}
return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
template<class T>
void print(const T a) { std::cout << a << '\n'; }
template<class Head, class... Tail>
void print(Head H, Tail... T) {
std::cout << H << ' ';
print(T...);
}
template<class T>
void printel(const T a) { std::cout << a << '\n'; }
template<class T>
void printel(const std::vector<T> &a) {
for (const auto &v : a)
std::cout << v << '\n';
}
template<class Head, class... Tail>
void printel(Head H, Tail... T) {
std::cout << H << '\n';
printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"
#define foa(v, a) for (auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x) for (int i = 0; i < (x); ++i)
#define rep2(i, l, r) for (int i = (l); i < (r); ++i)
#define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c))
#define repsname(a, b, c, ...) c
#define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x) for (int i = 1; i <= (x); ++i)
#define rrepname(a, b, c, ...) c
#define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x) for (int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
auto res = a;
UNIQUE(res);
for(auto &v : a)
v = lb(res, v);
return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
public:
cum_vector() = default;
template <class U>
cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
for(int i = 0; i < (int)vec.size(); i++)
cum[i + 1] = cum[i] + vec[i];
}
T prod(int l, int r) {
return cum[r] - cum[l];
}
private:
std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
const int n = s.size();
std::vector<std::pair<char, int>> ret;
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and s[l] == s[r]; r++) {}
ret.emplace_back(s[l], r - l);
l = r;
}
return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
int n = v.size();
std::vector<std::pair<T, int>> ret;
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and v[l] == v[r]; r++) {}
ret.emplace_back(v[l], r - l);
l = r;
}
return ret;
}
std::vector<int> iota(int n) {
std::vector<int> p(n);
std::iota(p.begin(), p.end(), 0);
return p;
}
#line 11 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 5 "h.cpp"
std::vector<bool> wildcard_pattern_matching(const std::vector<int> &p,
const std::vector<int> &s) {
using ll = long long;
using usize = std::size_t;
static constexpr int mod = 1811939329;
using mint = atcoder::static_modint<mod>;
const usize n = p.size();
const usize m = s.size();
assert(1 <= n);
assert(m <= m);
assert(n + m - 1 <= (mod - 1 & ~(mod - 1) + 1));
assert(std::all_of(p.begin(), p.end(), [](int x) { return -1 <= x < mod; }));
assert(std::all_of(s.begin(), s.end(), [](int x) { return -1 <= x < mod; }));
{
const int max = std::max(*std::max_element(p.begin(), p.end()),
*std::max_element(s.begin(), s.end()));
assert(ll(max) * max < mod);
assert(ll(max) * max * p.size() < mod);
}
std::vector<mint> sum(m - n + 1, mint(0));
const auto add = [&](const auto f, const auto g) {
std::vector<mint> x(n), y(m);
for(usize i = 0; i != n; ++i) {
x[i] = f(p[n - 1 - i]);
}
for(usize i = 0; i != m; ++i) {
y[i] = g(s[i]);
}
const auto z = atcoder::convolution(x, y);
for(usize i = 0; i != m - n + 1; ++i) {
sum[i] += z[n - 1 + i];
}
};
add([](const int v) { return ll(v != -1) * v * v; },
[](const int v) { return int(v != -1); });
add([](const int v) { return -2 * int(v != -1) * v; },
[](const int v) { return int(v != -1) * v; });
add([](const int v) { return int(v != -1); },
[](const int v) { return ll(v != -1) * v * v; });
std::vector<bool> res(m - n + 1);
for(usize i = 0; i != m - n + 1; ++i) {
res[i] = sum[i].val() == 0;
}
return res;
}
template <typename T>
struct rolling_hash {
private:
int n;
const long long mod = (1ll << 61) - 1;
const long long base = 1007;
std::vector<long long> hash, power;
long long mul(long long x, long long y) const {
return (__int128_t)x * y % mod;
}
public:
rolling_hash() = default;
rolling_hash(const T &s) : n((int)s.size()) {
hash.assign(n + 1, 0);
power.assign(n + 1, 1);
for(int i = 0; i < n; i++) {
hash[i + 1] = (mul(hash[i], base) + s[i]) % mod;
power[i + 1] = (mul(power[i], base)) % mod;
}
}
// get hash [l, r)
long long get(const int l, const int r) const {
assert(l <= r and l >= 0 and r <= n);
long long res = hash[r] - mul(hash[l], power[r - l]) % mod;
if(res < 0) res += mod;
return res;
}
// get hash [0, n)
long long get_all() const { return get(0, n); }
// return length of lcp (s[a, n), s[b, n))
int get_lcp(const int a, const int b) const {
assert(a >= 0 and a < n and b >= 0 and b < n);
int len = std::min(n - a, n - b), ok = 0, ng = len;
while(ng - ok > 1) {
int mid = (ok + ng) / 2;
if(get(a, a + mid) != get(b, b + mid))
ng = mid;
else
ok = mid;
}
return ok;
}
long long connect(ll h, ll p, ll plen) {
ll ret = (mul(h, power[plen]) + p) % mod;
if(ret < 0) ret += mod;
return ret;
}
};
void main_();
int main() {
INT(t);
while(t--) main_();
}
void main_() {
INT(n, m);
STR(s);
STR(t);
string sa = s;
foa(c, sa) if(c == '?') c = 'a';
const auto convert = [](const char c) -> int {
if(c == '?')
return -1;
else
return c - 'a';
};
V<> sv, tv;
foa(c, s) sv.pb(convert(c));
foa(c, t) tv.pb(convert(c));
auto wm = wildcard_pattern_matching(tv, sv);
// 貪欲は正しくないらしい こまった
// 完全に理解して sh[0:i]-t-sh[i+m:n] の辞書順比較をすればよいです
//
// sh と t が何文字一致しているか
// z-algo -> やっぱロリハ
rolling_hash th(t), sah(sa);
int ans = -1;
ll old = 0;
rrep(i, SZ(wm)) {
if(wm[i]) {
debug(i);
if(ans == -1)
ans = i;
else {
auto get = [&](int i, int x) -> ll {
// sh[0:i]-t-sh[i+m:n] の [0,x) hash
if(x <= i) {
return sah.get(0, x);
} else if(x <= i + SZ(t)) {
ll h1 = sah.get(0, i);
ll h2 = th.get(0, x - i);
return sah.connect(h1, h2, x - i);
} else {
ll h1 = sah.get(0, i);
ll h2 = th.get_all();
ll h12 = sah.connect(h1, h2, SZ(t));
ll len = x - i - SZ(t);
ll h3 = sah.get(i + SZ(t), i + SZ(t) + len);
return sah.connect(h12, h3, len);
}
};
ll ok = 0, ng = n;
auto f = [&](int m) {
return get(i, m) == get(ans, m);
};
if(f(ng)) continue;
//[0,x) は一緒
auto x = bin_search(ok, ng, f);
auto getchar = [&](int i, int x) -> ll {
// sh[0:i]-t-sh[i+m:n] の [0,x) hash
if(x < i) {
return sa[x];
} else if(x < i + SZ(t)) {
return t[x - i];
} else {
return sa[x];
}
};
debug(i, ans, x, getchar(i, x), getchar(ans, x));
if(getchar(ans, x) > getchar(i, x)) ans = i;
}
}
}
if(ans == -1)
print(-1);
else {
rep(j, m) {
sa[ans + j] = t[j];
}
print(sa);
}
}