結果
| 問題 |
No.3044 よくあるカエルさん
|
| ユーザー |
 横山緑
|
| 提出日時 | 2025-02-28 23:11:49 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 25,820 bytes |
| コンパイル時間 | 6,220 ms |
| コンパイル使用メモリ | 333,400 KB |
| 実行使用メモリ | 6,824 KB |
| 最終ジャッジ日時 | 2025-02-28 23:11:58 |
| 合計ジャッジ時間 | 7,003 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge6 |
（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
// competitive-verifier: PROBLEM
// https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
for(T &in : v)
is >> in;
return is;
}
template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64> vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for(auto &e : t)
fill_v(e, v);
}
template <typename F> struct FixPoint : F {
explicit FixPoint(F &&f) : F(std::forward<F>(f)) {
}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <typename F> inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{std::forward<F>(f)};
}
template <uint32_t mod_, bool fast = false> struct MontgomeryModInt {
private:
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_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(r * mod_ == 1, "invalid, r * mod != 1");
static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
public:
MontgomeryModInt() : x{} {
}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {
}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
}
mint &operator+=(const mint &p) {
if(i32(x += p.x - 2 * mod()) < 0)
x += 2 * mod();
return *this;
}
mint &operator-=(const mint &p) {
if(i32(x -= p.x) < 0)
x += 2 * mod();
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inv();
return *this;
}
mint operator-() const {
return mint() - *this;
}
mint operator+(const mint &p) const {
return mint(*this) += p;
}
mint operator-(const mint &p) const {
return mint(*this) -= p;
}
mint operator*(const mint &p) const {
return mint(*this) *= p;
}
mint operator/(const mint &p) const {
return mint(*this) /= p;
}
bool operator==(const mint &p) const {
return (x >= mod() ? x - mod() : x) ==
(p.x >= mod() ? p.x - mod() : p.x);
}
bool operator!=(const mint &p) const {
return (x >= mod() ? x - mod() : x) !=
(p.x >= mod() ? p.x - mod() : p.x);
}
u32 val() const {
u32 ret = reduce(x);
return ret >= mod() ? ret - mod() : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while(n > 0) {
if(n & 1)
ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inv() const {
return pow(mod() - 2);
}
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.val();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static constexpr u32 mod() {
return mod_;
}
};
template <uint32_t mod> using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
/**
* @brief Number Theoretic Transform Friendly ModInt
*/
template <typename Mint> struct NumberTheoreticTransformFriendlyModInt {
static vector<Mint> roots, iroots, rate3, irate3;
static int max_base;
NumberTheoreticTransformFriendlyModInt() = default;
static void init() {
if(roots.empty()) {
const unsigned mod = Mint::mod();
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0)
tmp >>= 1, max_base++;
Mint root = 2;
while(root.pow((mod - 1) >> 1) == 1) {
root += 1;
}
assert(root.pow(mod - 1) == 1);
roots.resize(max_base + 1);
iroots.resize(max_base + 1);
rate3.resize(max_base + 1);
irate3.resize(max_base + 1);
roots[max_base] = root.pow((mod - 1) >> max_base);
iroots[max_base] = Mint(1) / roots[max_base];
for(int i = max_base - 1; i >= 0; i--) {
roots[i] = roots[i + 1] * roots[i + 1];
iroots[i] = iroots[i + 1] * iroots[i + 1];
}
{
Mint prod = 1, iprod = 1;
for(int i = 0; i <= max_base - 3; i++) {
rate3[i] = roots[i + 3] * prod;
irate3[i] = iroots[i + 3] * iprod;
prod *= iroots[i + 3];
iprod *= roots[i + 3];
}
}
}
}
static void ntt(vector<Mint> &a) {
init();
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
int h = __builtin_ctz(n);
assert(h <= max_base);
int len = 0;
Mint imag = roots[2];
if(h & 1) {
int p = 1 << (h - 1);
Mint rot = 1;
for(int i = 0; i < p; i++) {
auto r = a[i + p];
a[i + p] = a[i] - r;
a[i] += r;
}
len++;
}
for(; len + 1 < h; len += 2) {
int p = 1 << (h - len - 2);
{ // s = 0
for(int i = 0; i < p; i++) {
auto a0 = a[i];
auto a1 = a[i + p];
auto a2 = a[i + 2 * p];
auto a3 = a[i + 3 * p];
auto a1na3imag = (a1 - a3) * imag;
auto a0a2 = a0 + a2;
auto a1a3 = a1 + a3;
auto a0na2 = a0 - a2;
a[i] = a0a2 + a1a3;
a[i + 1 * p] = a0a2 - a1a3;
a[i + 2 * p] = a0na2 + a1na3imag;
a[i + 3 * p] = a0na2 - a1na3imag;
}
}
Mint rot = rate3[0];
for(int s = 1; s < (1 << len); s++) {
int offset = s << (h - len);
Mint rot2 = rot * rot;
Mint rot3 = rot2 * rot;
for(int i = 0; i < p; i++) {
auto a0 = a[i + offset];
auto a1 = a[i + offset + p] * rot;
auto a2 = a[i + offset + 2 * p] * rot2;
auto a3 = a[i + offset + 3 * p] * rot3;
auto a1na3imag = (a1 - a3) * imag;
auto a0a2 = a0 + a2;
auto a1a3 = a1 + a3;
auto a0na2 = a0 - a2;
a[i + offset] = a0a2 + a1a3;
a[i + offset + 1 * p] = a0a2 - a1a3;
a[i + offset + 2 * p] = a0na2 + a1na3imag;
a[i + offset + 3 * p] = a0na2 - a1na3imag;
}
rot *= rate3[__builtin_ctz(~s)];
}
}
}
static void intt(vector<Mint> &a, bool f = true) {
init();
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
int h = __builtin_ctz(n);
assert(h <= max_base);
int len = h;
Mint iimag = iroots[2];
for(; len > 1; len -= 2) {
int p = 1 << (h - len);
{ // s = 0
for(int i = 0; i < p; i++) {
auto a0 = a[i];
auto a1 = a[i + 1 * p];
auto a2 = a[i + 2 * p];
auto a3 = a[i + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
auto a0na1 = a0 - a1;
auto a0a1 = a0 + a1;
auto a2a3 = a2 + a3;
a[i] = a0a1 + a2a3;
a[i + 1 * p] = (a0na1 + a2na3iimag);
a[i + 2 * p] = (a0a1 - a2a3);
a[i + 3 * p] = (a0na1 - a2na3iimag);
}
}
Mint irot = irate3[0];
for(int s = 1; s < (1 << (len - 2)); s++) {
int offset = s << (h - len + 2);
Mint irot2 = irot * irot;
Mint irot3 = irot2 * irot;
for(int i = 0; i < p; i++) {
auto a0 = a[i + offset];
auto a1 = a[i + offset + 1 * p];
auto a2 = a[i + offset + 2 * p];
auto a3 = a[i + offset + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
auto a0na1 = a0 - a1;
auto a0a1 = a0 + a1;
auto a2a3 = a2 + a3;
a[i + offset] = a0a1 + a2a3;
a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irot;
a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2;
a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3;
}
irot *= irate3[__builtin_ctz(~s)];
}
}
if(len >= 1) {
int p = 1 << (h - 1);
for(int i = 0; i < p; i++) {
auto ajp = a[i] - a[i + p];
a[i] += a[i + p];
a[i + p] = ajp;
}
}
if(f) {
Mint inv_sz = Mint(1) / n;
for(int i = 0; i < n; i++)
a[i] *= inv_sz;
}
}
static vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need)
nbase++;
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
Mint inv_sz = Mint(1) / sz;
for(int i = 0; i < sz; i++)
a[i] *= b[i] * inv_sz;
intt(a, false);
a.resize(need);
return a;
}
};
template <typename Mint>
vector<Mint> NumberTheoreticTransformFriendlyModInt<Mint>::roots =
vector<Mint>();
template <typename Mint>
vector<Mint> NumberTheoreticTransformFriendlyModInt<Mint>::iroots =
vector<Mint>();
template <typename Mint>
vector<Mint> NumberTheoreticTransformFriendlyModInt<Mint>::rate3 =
vector<Mint>();
template <typename Mint>
vector<Mint> NumberTheoreticTransformFriendlyModInt<Mint>::irate3 =
vector<Mint>();
template <typename Mint>
int NumberTheoreticTransformFriendlyModInt<Mint>::max_base = 0;
template <typename T> struct FormalPowerSeriesFriendlyNTT : vector<T> {
using vector<T>::vector;
using P = FormalPowerSeriesFriendlyNTT;
using NTT = NumberTheoreticTransformFriendlyModInt<T>;
P pre(int deg) const {
return P(begin(*this), begin(*this) + min((int)this->size(), deg));
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1)
ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
void shrink() {
while(this->size() && this->back() == T(0))
this->pop_back();
}
P operator+(const P &r) const {
return P(*this) += r;
}
P operator+(const T &v) const {
return P(*this) += v;
}
P operator-(const P &r) const {
return P(*this) -= r;
}
P operator-(const T &v) const {
return P(*this) -= v;
}
P operator*(const P &r) const {
return P(*this) *= r;
}
P operator*(const T &v) const {
return P(*this) *= v;
}
P operator/(const P &r) const {
return P(*this) /= r;
}
P operator%(const P &r) const {
return P(*this) %= r;
}
P &operator+=(const P &r) {
if(r.size() > this->size())
this->resize(r.size());
for(int i = 0; i < (int)r.size(); i++)
(*this)[i] += r[i];
return *this;
}
P &operator-=(const P &r) {
if(r.size() > this->size())
this->resize(r.size());
for(int i = 0; i < (int)r.size(); i++)
(*this)[i] -= r[i];
return *this;
}
// https://judge.yosupo.jp/problem/convolution_mod
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
auto ret = NTT::multiply(*this, r);
return *this = {begin(ret), end(ret)};
}
P &operator/=(const P &r) {
if(this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P &operator%=(const P &r) {
*this -= *this / r * r;
shrink();
return *this;
}
// https://judge.yosupo.jp/problem/division_of_polynomials
pair<P, P> div_mod(const P &r) {
P q = *this / r;
P x = *this - q * r;
x.shrink();
return make_pair(q, x);
}
P operator-() const {
P ret(this->size());
for(int i = 0; i < (int)this->size(); i++)
ret[i] = -(*this)[i];
return ret;
}
P &operator+=(const T &r) {
if(this->empty())
this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const T &r) {
if(this->empty())
this->resize(1);
(*this)[0] -= r;
return *this;
}
P &operator*=(const T &v) {
for(int i = 0; i < (int)this->size(); i++)
(*this)[i] *= v;
return *this;
}
P dot(P r) const {
P ret(min(this->size(), r.size()));
for(int i = 0; i < (int)ret.size(); i++)
ret[i] = (*this)[i] * r[i];
return ret;
}
P operator>>(int sz) const {
if((int)this->size() <= sz)
return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
T operator()(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
P diff() const {
const int n = (int)this->size();
P ret(max(0, n - 1));
for(int i = 1; i < n; i++)
ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int)this->size();
P ret(n + 1);
ret[0] = T(0);
for(int i = 0; i < n; i++)
ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
// https://judge.yosupo.jp/problem/inv_of_formal_power_series
// F(0) must not be 0
P inv(int deg = -1) const {
assert(((*this)[0]) != T(0));
const int n = (int)this->size();
if(deg == -1)
deg = n;
P res(deg);
res[0] = {T(1) / (*this)[0]};
for(int d = 1; d < deg; d <<= 1) {
P f(2 * d), g(2 * d);
for(int j = 0; j < min(n, 2 * d); j++)
f[j] = (*this)[j];
for(int j = 0; j < d; j++)
g[j] = res[j];
NTT::ntt(f);
NTT::ntt(g);
f = f.dot(g);
NTT::intt(f);
for(int j = 0; j < d; j++)
f[j] = 0;
NTT::ntt(f);
for(int j = 0; j < 2 * d; j++)
f[j] *= g[j];
NTT::intt(f);
for(int j = d; j < min(2 * d, deg); j++)
res[j] = -f[j];
}
return res;
}
// https://judge.yosupo.jp/problem/log_of_formal_power_series
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == T(1));
const int n = (int)this->size();
if(deg == -1)
deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
// https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
P sqrt(
int deg = -1,
const function<T(T)> &get_sqrt = [](T) { return T(1); }) const {
const int n = (int)this->size();
if(deg == -1)
deg = n;
if((*this)[0] == T(0)) {
for(int i = 1; i < n; i++) {
if((*this)[i] != T(0)) {
if(i & 1)
return {};
if(deg - i / 2 <= 0)
break;
auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
if(ret.empty())
return {};
ret = ret << (i / 2);
if((int)ret.size() < deg)
ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
auto sqr = T(get_sqrt((*this)[0]));
if(sqr * sqr != (*this)[0])
return {};
P ret{sqr};
T inv2 = T(1) / T(2);
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
}
return ret.pre(deg);
}
P sqrt(const function<T(T)> &get_sqrt, int deg = -1) const {
return sqrt(deg, get_sqrt);
}
// https://judge.yosupo.jp/problem/exp_of_formal_power_series
// F(0) must be 0
P exp(int deg = -1) const {
if(deg == -1)
deg = this->size();
assert((*this)[0] == T(0));
P inv;
inv.reserve(deg + 1);
inv.push_back(T(0));
inv.push_back(T(1));
auto inplace_integral = [&](P &F) -> void {
const int n = (int)F.size();
auto mod = T::mod();
while((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), T(0));
for(int i = 1; i <= n; i++)
F[i] *= inv[i];
};
auto inplace_diff = [](P &F) -> void {
if(F.empty())
return;
F.erase(begin(F));
T coeff = 1, one = 1;
for(int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
P b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for(int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
NTT::ntt(y);
z1 = z2;
P z(m);
for(int i = 0; i < m; ++i)
z[i] = y[i] * z1[i];
NTT::intt(z);
fill(begin(z), begin(z) + m / 2, T(0));
NTT::ntt(z);
for(int i = 0; i < m; ++i)
z[i] *= -z1[i];
NTT::intt(z);
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
NTT::ntt(z2);
P x(begin(*this), begin(*this) + min<int>(this->size(), m));
inplace_diff(x);
x.push_back(T(0));
NTT::ntt(x);
for(int i = 0; i < m; ++i)
x[i] *= y[i];
NTT::intt(x);
x -= b.diff();
x.resize(2 * m);
for(int i = 0; i < m - 1; ++i)
x[m + i] = x[i], x[i] = T(0);
NTT::ntt(x);
for(int i = 0; i < 2 * m; ++i)
x[i] *= z2[i];
NTT::intt(x);
x.pop_back();
inplace_integral(x);
for(int i = m; i < min<int>(this->size(), 2 * m); ++i)
x[i] += (*this)[i];
fill(begin(x), begin(x) + m, T(0));
NTT::ntt(x);
for(int i = 0; i < 2 * m; ++i)
x[i] *= y[i];
NTT::intt(x);
b.insert(end(b), begin(x) + m, end(x));
}
return P{begin(b), begin(b) + deg};
}
// https://judge.yosupo.jp/problem/pow_of_formal_power_series
P pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if(deg == -1)
deg = n;
if(k == 0) {
P ret(deg, T(0));
ret[0] = T(1);
return ret;
}
for(int i = 0; i < n; i++) {
if(i * k > deg)
return P(deg, T(0));
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P ret = (((*this * rev) >> i).log() * k).exp() *
((*this)[i].pow(k));
ret = (ret << (i * k)).pre(deg);
if((int)ret.size() < deg)
ret.resize(deg, T(0));
return ret;
}
}
return *this;
}
P mod_pow(int64_t k, P g) const {
P modinv = g.rev().inv();
auto get_div = [&](P base) {
if(base.size() < g.size()) {
base.clear();
return base;
}
int n = base.size() - g.size() + 1;
return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
};
P x(*this), ret{1};
while(k > 0) {
if(k & 1) {
ret *= x;
ret -= get_div(ret) * g;
ret.shrink();
}
x *= x;
x -= get_div(x) * g;
x.shrink();
k >>= 1;
}
return ret;
}
// https://judge.yosupo.jp/problem/polynomial_taylor_shift
P taylor_shift(T c) const {
int n = (int)this->size();
vector<T> fact(n), rfact(n);
fact[0] = rfact[0] = T(1);
for(int i = 1; i < n; i++)
fact[i] = fact[i - 1] * T(i);
rfact[n - 1] = T(1) / fact[n - 1];
for(int i = n - 1; i > 1; i--)
rfact[i - 1] = rfact[i] * T(i);
P p(*this);
for(int i = 0; i < n; i++)
p[i] *= fact[i];
p = p.rev();
P bs(n, T(1));
for(int i = 1; i < n; i++)
bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
p = (p * bs).pre(n);
p = p.rev();
for(int i = 0; i < n; i++)
p[i] *= rfact[i];
return p;
}
};
template <typename Mint> using FPS = FormalPowerSeriesFriendlyNTT<Mint>;
/**
* @brief Coeff of Rational Function
*
*/
template <template <typename> class FPS, typename Mint>
Mint coeff_of_rational_function(FPS<Mint> P, FPS<Mint> Q, int64_t k) {
// compute the coefficient [x^k] P/Q of rational power series
Mint ret = 0;
if(P.size() >= Q.size()) {
auto R = P / Q;
P -= R * Q;
P.shrink();
if(k < (int)R.size())
ret += R[k];
}
if(P.empty())
return ret;
P.resize((int)Q.size() - 1);
auto sub = [&](const FPS<Mint> &as, bool odd) {
FPS<Mint> bs((as.size() + !odd) / 2);
for(int i = odd; i < (int)as.size(); i += 2)
bs[i >> 1] = as[i];
return bs;
};
while(k > 0) {
auto Q2(Q);
for(int i = 1; i < (int)Q2.size(); i += 2)
Q2[i] = -Q2[i];
P = sub(P * Q2, k & 1);
Q = sub(Q * Q2, 0);
k >>= 1;
}
return ret + P[0];
}
/**
* @brief Kth Term of Linearly Recurrent Sequence
*
*/
template <template <typename> class FPS, typename Mint>
Mint kth_term_of_linearly_recurrent_sequence(const FPS<Mint> &a, FPS<Mint> c,
int64_t k) {
assert(a.size() == c.size());
c = FPS<Mint>{1} - (c << 1);
return coeff_of_rational_function((a * c).pre(a.size()), c, k);
}
using mint = modint998244353;
// https://ei1333.github.io/library/math/fps/kth-term-of-linearly-recurrent-sequence.hpp
int main() {
int n, t, k, l;
cin >> n >> t >> k >> l;
FPS<mint> p(1), q(t + 1);
p[0] = q[0] = 1;
q[1] = -mint(k - 1) / 6;
q[2] = -mint(l - k) / 6;
q[t] = -mint(7 - l) / 6;
// cout << p << endl;
// cout << q << endl;
// int D;
// int64_t K;
// cin >> D >> K;
// FPS<mint> a(D), c(D);
// cin >> a >> c;
cout << coeff_of_rational_function(p, q, n - 1) << "\n";
}