結果
| 問題 |
No.3370 AB → BA
|
| コンテスト | |
| ユーザー |
 Rubikun
|
| 提出日時 | 2025-11-17 23:49:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 904 ms / 2,000 ms |
| コード長 | 31,309 bytes |
| コンパイル時間 | 3,883 ms |
| コンパイル使用メモリ | 249,016 KB |
| 実行使用メモリ | 23,252 KB |
| 最終ジャッジ日時 | 2025-11-17 23:49:22 |
| 合計ジャッジ時間 | 11,358 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 20 |
ソースコード
// https://judge.yosupo.jp/submission/319327
#include <bits/stdc++.h>
using namespace std;
#include<vector>
#include<assert.h>
//modint+畳み込み+逆元テーブル
// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
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
#include <utility>
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
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;
}
};
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;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
for (long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
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};
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
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
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
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
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
using mint=atcoder::modint998244353;
namespace po167{
template<class T>
struct Binomial{
std::vector<T> fact_vec, fact_inv_vec;
void extend(int m = -1){
int n = fact_vec.size();
if (m == -1) m = n * 2;
if (n >= m) return;
fact_vec.resize(m);
fact_inv_vec.resize(m);
for (int i = n; i < m; i++){
fact_vec[i] = fact_vec[i - 1] * T(i);
}
fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1];
for (int i = m - 1; i > n; i--){
fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i);
}
}
Binomial(int MAX = 0){
fact_vec.resize(1, T(1));
fact_inv_vec.resize(1, T(1));
extend(MAX + 1);
}
T fact(int i){
if (i < 0) return 0;
while (int(fact_vec.size()) <= i) extend();
return fact_vec[i];
}
T invfact(int i){
if (i < 0) return 0;
while (int(fact_inv_vec.size()) <= i) extend();
return fact_inv_vec[i];
}
T C(int a, int b){
if (a < b || b < 0) return 0;
return fact(a) * invfact(b) * invfact(a - b);
}
T invC(int a, int b){
if (a < b || b < 0) return 0;
return fact(b) * fact(a - b) *invfact(a);
}
T P(int a, int b){
if (a < b || b < 0) return 0;
return fact(a) * invfact(a - b);
}
T inv(int a){
if (a < 0) return inv(-a) * T(-1);
if (a == 0) return 1;
return fact(a - 1) * invfact(a);
}
T Catalan(int n){
if (n < 0) return 0;
return fact(2 * n) * invfact(n + 1) * invfact(n);
}
T narayana(int n, int k){
if (n <= 0 || n < k || k < 1) return 0;
return C(n, k) * C(n, k - 1) * inv(n);
}
T Catalan_pow(int n,int d){
if (n < 0 || d < 0) return 0;
if (d == 0){
if (n == 0) return 1;
return 0;
}
return T(d) * inv(d + n) * C(2 * n + d - 1, n);
}
// retrun [x^a] 1/(1-x)^b
T ruiseki(int a,int b){
if (a < 0 || b < 0) return 0;
if (a == 0){
return 1;
}
return C(a + b - 1, b - 1);
}
// (a, b) -> (c, d)
// always x + e >= y
T mirror(int a, int b, int c, int d, int e = 0){
if (a + e < b || c + e < d) return 0;
if (a > c || b > d) return 0;
a += e;
c += e;
return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1);
}
// return sum_{i = 0, ... , a} sum_{j = 0, ... , b} C(i + j, i)
// return C(a + b + 2, a + 1) - 1;
T gird_sum(int a, int b){
if (a < 0 || b < 0) return 0;
return C(a + b + 2, a + 1) - 1;
}
// return sum_{i = a, ..., b - 1} sum_{j = c, ... , d - 1} C(i + j, i)
// AGC 018 E
T gird_sum_2(int a, int b, int c, int d){
if (a >= b || c >= d) return 0;
a--, b--, c--, d--;
return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d);
}
// the number of diagonal dissections of a convex n-gon into k+1 regions.
// OEIS A033282
// AGC065D
T diagonal(int n, int k){
if (n <= 2 || n - 3 < k || k < 0) return 0;
return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1);
}
};
}
#line 4 "fps/FPS_cyclic_convolution.hpp"
namespace po167{
// |f| = |g| = 2 ^ n
template<class T>
std::vector<T> FPS_cyclic_convolution(std::vector<T> f, std::vector<T> g){
atcoder::internal::butterfly(f);
atcoder::internal::butterfly(g);
for (int i = 0; i < (int)f.size(); i++) f[i] *= g[i];
atcoder::internal::butterfly_inv(f);
T iz = (T)(1) / (T)(f.size());
for (int i = 0; i < (int)f.size(); i++) f[i] *= iz;
return f;
}
}
#line 5 "fps/count_increasing_sequences.hpp"
namespace po167{
template<class T>
std::pair<std::vector<T>, std::vector<T>> count_square(std::vector<T> L, std::vector<T> D){
assert(!L.empty() && !D.empty());
int N = L.size();
int M = D.size();
if (std::min(N, M) <= 200){
int sw = 0;
if (N > M) std::swap(N, M), std::swap(L, D), sw = 1;
std::vector<T> R(N);
for (int i = 0; i < N; i++){
D[0] += L[i];
for (int j = 1; j < M; j++) D[j] += D[j - 1];
R[i] = D.back();
}
if (sw) std::swap(R, D);
return {R, D};
}
po167::Binomial<T> table(N + M);
std::vector<T> R(N), U(M);
int z = 0;
while ((1 << z) < (N + M - 1)) z++;
// 左から右
{
std::vector<T> tmp(N);
for (int i = 0; i < N; i++) tmp[i] = table.C(M - 1 + i, i);
tmp = atcoder::convolution(tmp, L);
for (int i = 0; i < N; i++) R[i] += tmp[i];
}
// 左から上
{
std::vector<T> tmp(1 << z);
for (int i = 0; i < N; i++) L[i] *= table.invfact(N - 1 - i);
for (int i = 0; i < N + M - 1; i++) tmp[i] = table.fact(i);
L.resize(1 << z, 0);
tmp = po167::FPS_cyclic_convolution(tmp, L);
for (int i = 0; i < M; i++) U[i] += tmp[N - 1 + i] * table.invfact(i);
}
// 下から上
{
std::vector<T> tmp(M);
for (int i = 0; i < M; i++) tmp[i] = table.C(N - 1 + i, i);
tmp = atcoder::convolution(tmp, D);
for (int i = 0; i < M; i++) U[i] += tmp[i];
}
// 下から右
{
std::vector<T> tmp(1 << z);
for (int i = 0; i < M; i++) D[i] *= table.invfact(M - i - 1);
for (int i = 0; i < N + M - 1; i++) tmp[i] = table.fact(i);
D.resize(1 << z, 0);
tmp = po167::FPS_cyclic_convolution(tmp, D);
for (int i = 0; i < N; i++) R[i] += tmp[M - 1 + i] * table.invfact(i);
}
return {R, U};
}
template<class T>
/*
* g(A, x) を
* 0 <= B[i] < A[i] かつ B[i] = x を満たす
* 広義単調増加列 B の数とする
* res[x] = sum C[i] * g(A[i:N], x)
* を返す
*/
std::vector<T> count_increase_sequences_with_upper_bounds(std::vector<int> A, std::vector<T> C){
int N = A.size();
assert((int)C.size() == N);
assert(N);
for (int i = (int)(A.size()) - 1; i > 0; i--) A[i - 1] = std::min(A[i - 1], A[i]);
if (A.back() == 0) return {};
if (std::min(A.back(), N) <= 200){
std::vector<T> dp(0);
dp.reserve(A.back());
for (int i = 0; i < N; i++){
dp.resize(A[i], 0);
if (A[i]) dp[0] += C[i];
for (int j = 1; j < (int)dp.size(); j++){
dp[j] += dp[j - 1];
}
}
return dp;
}
if (N == 1){
std::vector<T> res(A[0]);
for (int i = 0; i < A[0]; i++) res[i] = C[0];
return res;
}
int m = N / 2;
std::vector<int> LA(m), RA(N - m);
std::vector<T> LC(m), RC(N - m);
for (int i = 0; i < m; i++){
LA[i] = A[i];
LC[i] = C[i];
}
for (int i = 0; i < N - m; i++){
RA[i] = A[i + m] - A[m - 1];
RC[i] = C[i + m];
}
std::vector<T> res;
res.reserve(A.back());
auto L = count_increase_sequences_with_upper_bounds(LA, LC);
if (!L.empty()){
auto [R, U] = count_square(L, RC);
for (int i = 0; i < (int)R.size(); i++) res.push_back(R[i]);
std::swap(U, RC);
}
auto R = count_increase_sequences_with_upper_bounds(RA, RC);
for (auto x : R) res.push_back(x);
return res;
}
template<class T>
std::vector<T> NAIVE_count_increase_sequences_with_upper_lower_bounds(std::vector<int> A, std::vector<int> B, std::vector<T> C = {}){
std::vector<T> tmp(B.back() - A[0]);
if (C.empty()){
int b = B[0];
for (int i = 1; i < (int)B.size(); i++) b = std::min(b, B[i]);
for (int i = 0; i < b - A[0]; i++) tmp[i] = 1;
}
else for (int i = 0; i < (int)std::min(tmp.size(), C.size()); i++) tmp[i] = C[i];
int N = A.size();
for (int i = 1; i < N; i++){
for (int j = 1; j < (int)tmp.size(); j++){
tmp[j] += tmp[j - 1];
}
for (int j = 0; j < (int)tmp.size(); j++){
if (j < A[i] - A[0] || B[i] - A[0] <= j) tmp[j] = 0;
}
}
std::vector<T> res(B.back() - A.back());
for (int i = 0; i < B.back() - A.back(); i++){
res[i] = tmp[A.back() - A[0] + i];
}
return res;
}
template<class T>
/*
* f(a, b) を X[0] = a, X[N - 1] = b であるような、A, B に挟まれたものとする
* 長さ B[N - 1] - A[N - 1] を返す
* res[b - A.back()] = sum C[a - A[0]] * f(a, b)
* A, B は広義単調増加が嬉しい
*/
std::vector<T> count_increase_sequences_with_upper_lower_bounds(std::vector<int> A, std::vector<int> B, std::vector<T> C = {}){
int N = A.size();
assert(A.size() == B.size());
for (int i = 0; i < N - 1; i++){
A[i + 1] = std::max(A[i], A[i + 1]);
}
for (int i = N - 1; i > 0; i--){
B[i - 1] = std::min(B[i], B[i - 1]);
}
if (A.back() >= B.back()) return {};
// A[0] == 0 にする
std::vector<T> res(B.back() - A.back(), 0);
{
int tmp = A[0];
for (int i = 0; i < N; i++){
A[i] -= tmp;
B[i] -= tmp;
if (A[i] >= B[i]) return res;
}
}
if (C.empty()){
C.resize(B[0] - A[0], 1);
}
else assert((int)(C.size()) == B[0] - A[0]);
int l = 0;
while (B[l] <= A.back()){
for (int i = (int)(C.size()) - 1; i > 0; i--) C[i] -= C[i - 1];
int nl = l;
while (A[nl] < B[l]) nl++;
std::vector<int> tmp(B[l] - A[l]);
tmp[0] = 1;
for (int i = l; i < nl; i++){
tmp[A[i] - A[l]]++;
}
for (int i = 1; i < B[l] - A[l]; i++) tmp[i] += tmp[i - 1];
auto X = count_increase_sequences_with_upper_bounds(tmp, C);
std::vector<int> nB(nl - l + 1);
for (int i = l; i <= nl; i++){
nB[i - l] = B[i] - B[l];
}
auto Y = count_increase_sequences_with_upper_bounds(nB, X);
C.resize(B[nl] - A[nl]);
for (int i = 0; i < B[nl] - A[nl]; i++){
C[i] = Y[i + A[nl] - B[l]];
}
l = nl;
}
// A を揃えてしまえ
{
int a = A[l];
for (int i = l; i < N; i++){
A[i] -= a;
B[i] -= a;
}
}
for (int i = (int)(C.size()) - 1; i > 0; i--) C[i] -= C[i - 1];
std::vector<T> D(N - l, 0);
if (A.back() != 0){
std::vector<T> L(A.back());
for (int i = 0; i < (int)L.size(); i++) L[i] = C[i];
std::vector<int> tmp(L.size());
tmp[0] = 1;
for (int i = l; i < N; i++){
if (A[i] < (int)tmp.size()) tmp[A[i]]++;
}
for (int i = 1; i < (int)tmp.size(); i++){
tmp[i] += tmp[i - 1];
}
auto nD = count_increase_sequences_with_upper_bounds(tmp, L);
for (int i = 0; i < (int)nD.size(); i++) D[i] = nD[i];
}
for (int i = A.back(); i < B[l]; i++) C[i - A.back()] = C[i];
C.resize(B[l] - A.back());
auto [R, U] = count_square(C, D);
res = R;
std::vector<int> nB(N - l);
for (int i = 0; i < N - l; i++) nB[i] = B[i + l] - B[l];
R = count_increase_sequences_with_upper_bounds(nB, U);
for (auto x : R) res.push_back(x);
return res;
}
}
#line 2 "a.cpp"
#include <iostream>
int main() {
string S;cin>>S;
int la=-1;
vector<int> A,B;
for(int i=0;i<S.size();i++){
if(S[i]=='A'){
A.push_back(0);
B.push_back(i-la-1);
la=i;
}
}
for(int i=1;i<B.size();i++) B[i]+=B[i-1];
for(int i=0;i<B.size();i++) B[i]++;
if(A.size()==0){
cout<<1<<"\n";
}else{
int N=A.size();
int M=B.back()+1;
using mint = atcoder::modint998244353;
auto tmp = po167::count_increase_sequences_with_upper_lower_bounds<mint>(A, B);
mint ans = 0;
for (auto x : tmp) ans += x;
std::cout << ans.val() << "\n";
}
}