結果
問題 | No.2231 Surprising Flash! |
ユーザー |
![]() |
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 |
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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>#endifnamespace 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_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __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>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr 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 Lakestruct 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 munsigned 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 + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned 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/gconstexpr 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| <= blong 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| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (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) <= nn = (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_VERtemplate <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;#elsetemplate <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;#endiftemplate <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 internaltemplate <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) == 1std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1std::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 transformedwhile (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-baseint 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 transformedwhile (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-baseint 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 internaltemplate <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; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static 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 = 4long 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 Constructiontemplate <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 internalstd::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// Applicationstemplate <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 Biologytemplate <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";elsestd::cerr << e;}void view(const int &e) {if(e == inf)std::cerr << "inf";else if(e == -inf)std::cerr << "-inf";elsestd::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 LOCALvoid 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;elseok = 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;elsereturn 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) hashif(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) hashif(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);}}