#pragma once
#include <vector>
using namespace std;
#include "../modint/montgomery-modint.hpp"
#include "../ntt/ntt.hpp"
namespace WildcardPatternMatchingImpl {
template <typename Container, unsigned int MOD>
vector<int> inner(const Container& a, const Container& b,
const typename Container::value_type& wildcard = 0) {
using mint = LazyMontgomeryModInt<MOD>;
static NTT<mint> ntt;
int N = a.size(), M = b.size();
vector<mint> A1(N), A2(N), A3(N), B1(M), B2(M), B3(M);
for (int i = 0; i < N; i++) {
mint x = a[i] == wildcard ? 0 : a[i];
mint y = a[i] == wildcard ? 0 : 1;
A1[i] = y * x * x;
A2[i] = y * x * (-2);
A3[i] = y;
}
for (int i = 0; i < M; i++) {
mint x = b[i] == wildcard ? 0 : b[i];
mint y = b[i] == wildcard ? 0 : 1;
B1[M - 1 - i] = y;
B2[M - 1 - i] = y * x;
B3[M - 1 - i] = y * x * x;
}
auto AB1 = ntt.multiply(A1, B1);
auto AB2 = ntt.multiply(A2, B2);
auto AB3 = ntt.multiply(A3, B3);
vector<int> res(N - M + 1, 1);
for (int i = 0; i < N - M + 1; i++) {
mint x = AB1[i + M - 1] + AB2[i + M - 1] + AB3[i + M - 1];
if (x != 0) res[i] = 0;
}
return res;
}
// 返り値 : 長さ |a| - |b| + 1 の配列 c
// c[i] := a[i, i+|b|) b とマッチするならば 1, しなければ 0)
// wildcard は引数に入れる (default で 0)
template <typename Container>
vector<int> wildcard_pattern_matching(
const Container& a, const Container& b,
const typename Container::value_type& wildcard = 0) {
if ((int)b.size() == 0) return vector<int>(a.size() + 1, 1);
if (a.size() < b.size()) return {};
vector<int> res1 = inner<Container, 998244353>(a, b, wildcard);
vector<int> res2 = inner<Container, 924844033>(a, b, wildcard);
vector<int> res3 = inner<Container, 1012924417>(a, b, wildcard);
for (int i = 0; i < (int)res1.size(); i++) res1[i] &= res2[i] & res3[i];
return res1;
}
} // namespace WildcardPatternMatchingImpl
using WildcardPatternMatchingImpl::wildcard_pattern_matching;
/**
* @brief Wildcard Pattern Matching
*/
#line 2 "string/wildcard-pattern-matching.hpp"
#include <vector>
using namespace std;
#line 2 "modint/montgomery-modint.hpp"
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
#line 2 "ntt/ntt.hpp"
template <typename mint>
struct NTT {
static constexpr uint32_t get_pr() {
uint32_t _mod = mint::get_mod();
using u64 = uint64_t;
u64 ds[32] = {};
int idx = 0;
u64 m = _mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t _pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % _mod;
a = a * a % _mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++_pr;
}
return _pr;
};
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = get_pr();
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
NTT() { setwy(level); }
void fft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
}
}
// jh >= 1
mint ww = one, xx = one * dw[2], wx = one;
for (int jh = 4; jh < u;) {
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
}
xx *= dw[__builtin_ctzll((jh += 4))];
}
u <<= 2;
v >>= 2;
}
}
void ifft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
}
}
// jh >= 1
mint ww = one, xx = one * dy[2], yy = one;
u <<= 2;
for (int jh = 4; jh < u;) {
ww = xx * xx, yy = xx * imag;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
}
xx *= dy[__builtin_ctzll(jh += 4)];
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
u = 1 << (k - 1);
for (int j = 0; j < u; ++j) {
mint ajv = a[j] - a[j + u];
a[j] += a[j + u];
a[j + u] = ajv;
}
}
}
void ntt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
fft4(a, __builtin_ctz(a.size()));
}
void intt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
ifft4(a, __builtin_ctz(a.size()));
mint iv = mint(a.size()).inverse();
for (auto &x : a) x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while (M < l) M <<= 1, ++k;
setwy(k);
vector<mint> s(M);
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
fft4(s, k);
if (a.size() == b.size() && a == b) {
for (int i = 0; i < M; ++i) s[i] *= s[i];
} else {
vector<mint> t(M);
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
fft4(t, k);
for (int i = 0; i < M; ++i) s[i] *= t[i];
}
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
ntt(b);
copy(begin(b), end(b), back_inserter(a));
}
};
#line 8 "string/wildcard-pattern-matching.hpp"
namespace WildcardPatternMatchingImpl {
template <typename Container, unsigned int MOD>
vector<int> inner(const Container& a, const Container& b,
const typename Container::value_type& wildcard = 0) {
using mint = LazyMontgomeryModInt<MOD>;
static NTT<mint> ntt;
int N = a.size(), M = b.size();
vector<mint> A1(N), A2(N), A3(N), B1(M), B2(M), B3(M);
for (int i = 0; i < N; i++) {
mint x = a[i] == wildcard ? 0 : a[i];
mint y = a[i] == wildcard ? 0 : 1;
A1[i] = y * x * x;
A2[i] = y * x * (-2);
A3[i] = y;
}
for (int i = 0; i < M; i++) {
mint x = b[i] == wildcard ? 0 : b[i];
mint y = b[i] == wildcard ? 0 : 1;
B1[M - 1 - i] = y;
B2[M - 1 - i] = y * x;
B3[M - 1 - i] = y * x * x;
}
auto AB1 = ntt.multiply(A1, B1);
auto AB2 = ntt.multiply(A2, B2);
auto AB3 = ntt.multiply(A3, B3);
vector<int> res(N - M + 1, 1);
for (int i = 0; i < N - M + 1; i++) {
mint x = AB1[i + M - 1] + AB2[i + M - 1] + AB3[i + M - 1];
if (x != 0) res[i] = 0;
}
return res;
}
// 返り値 : 長さ |a| - |b| + 1 の配列 c
// c[i] := a[i, i+|b|) b とマッチするならば 1, しなければ 0)
// wildcard は引数に入れる (default で 0)
template <typename Container>
vector<int> wildcard_pattern_matching(
const Container& a, const Container& b,
const typename Container::value_type& wildcard = 0) {
if ((int)b.size() == 0) return vector<int>(a.size() + 1, 1);
if (a.size() < b.size()) return {};
vector<int> res1 = inner<Container, 998244353>(a, b, wildcard);
vector<int> res2 = inner<Container, 924844033>(a, b, wildcard);
vector<int> res3 = inner<Container, 1012924417>(a, b, wildcard);
for (int i = 0; i < (int)res1.size(); i++) res1[i] &= res2[i] & res3[i];
return res1;
}
} // namespace WildcardPatternMatchingImpl
using WildcardPatternMatchingImpl::wildcard_pattern_matching;
/**
* @brief Wildcard Pattern Matching
*/
Wildcard Pattern Matching