結果
| 問題 | No.2883 K-powered Sum of Fibonacci |
| ユーザー |
 Fu_L
|
| 提出日時 | 2025-02-10 01:12:16 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 292 ms / 3,000 ms |
| コード長 | 25,119 bytes |
| コンパイル時間 | 4,126 ms |
| コンパイル使用メモリ | 297,696 KB |
| 実行使用メモリ | 30,612 KB |
| 最終ジャッジ日時 | 2025-02-10 01:12:28 |
| 合計ジャッジ時間 | 12,306 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 40 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
SetupIO() {
ios::sync_with_stdio(0);
cin.tie(0);
cout << fixed << setprecision(30);
}
} setup_io;
template <uint32_t m>
struct StaticModint {
using mint = StaticModint;
static constexpr uint32_t mod() {
return m;
}
static constexpr mint raw(const uint32_t v) {
mint a;
a._v = v;
return a;
}
constexpr StaticModint()
: _v(0) {}
template <class T>
constexpr StaticModint(const T& v) {
static_assert(is_integral_v<T>);
if constexpr(is_signed_v<T>) {
int64_t x = int64_t(v % int64_t(m));
if(x < 0) x += m;
_v = uint32_t(x);
} else _v = uint32_t(v % m);
}
constexpr uint32_t val() const {
return _v;
}
constexpr mint& operator++() {
return *this += 1;
}
constexpr mint& operator--() {
return *this -= 1;
}
constexpr mint operator++(int) {
mint res = *this;
++*this;
return res;
}
constexpr mint operator--(int) {
mint res = *this;
--*this;
return res;
}
constexpr mint& operator+=(mint rhs) {
if(_v >= m - rhs._v) _v -= m;
_v += rhs._v;
return *this;
}
constexpr mint& operator-=(mint rhs) {
if(_v < rhs._v) _v += m;
_v -= rhs._v;
return *this;
}
constexpr mint& operator*=(mint rhs) {
return *this = *this * rhs;
}
constexpr mint& operator/=(mint rhs) {
return *this *= rhs.inv();
}
constexpr mint operator+() const {
return *this;
}
constexpr mint operator-() const {
return mint{} - *this;
}
constexpr mint pow(long long n) const {
assert(0 <= n);
if(n == 0) return 1;
mint x = *this, r = 1;
while(1) {
if(n & 1) r *= x;
n >>= 1;
if(n == 0) return r;
x *= x;
}
}
constexpr mint inv() const {
if constexpr(prime) {
assert(_v);
return pow(m - 2);
} else {
const auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(mint lhs, mint rhs) {
return lhs += rhs;
}
friend constexpr mint operator-(mint lhs, mint rhs) {
return lhs -= rhs;
}
friend constexpr mint operator*(mint lhs, mint rhs) {
return uint64_t(lhs._v) * rhs._v;
}
friend constexpr mint operator/(mint lhs, mint rhs) {
return lhs /= rhs;
}
friend constexpr bool operator==(mint lhs, mint rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(mint lhs, mint rhs) {
return lhs._v != rhs._v;
}
friend istream& operator>>(istream& in, mint& x) {
long long a;
in >> a;
x = a;
return in;
}
friend ostream& operator<<(ostream& out, const mint& x) {
return out << x.val();
}
private:
uint32_t _v = 0;
static constexpr bool prime = []() -> bool {
if(m == 1) return 0;
if(m == 2 or m == 7 or m == 61) return 1;
if(m % 2 == 0) return 0;
uint32_t d = m - 1;
while(d % 2 == 0) d /= 2;
for(uint32_t a : {2, 7, 61}) {
uint32_t t = d;
mint y = mint(a).pow(t);
while(t != m - 1 && y != 1 && y != m - 1) {
y *= y;
t <<= 1;
}
if(y != m - 1 && t % 2 == 0) return 0;
}
return 1;
}();
static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
if(a == 0) return {b, 0};
int32_t s = b, t = a, m0 = 0, m1 = 1;
while(t) {
const int32_t u = s / t;
s -= t * u;
m0 -= m1 * u;
swap(s, t);
swap(m0, m1);
}
if(m0 < 0) m0 += b / s;
return {s, m0};
}
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
using mint = modint998244353;
constexpr long long pow_mod(long long x, long long n, const long long mod) {
assert(n >= 0 and mod >= 1);
x %= mod;
if(x < 0) x += mod;
long long res = 1;
while(n > 0) {
if(n & 1) res = res * x % mod;
x = x * x % mod;
n >>= 1;
}
return res;
}
constexpr int primitive_root(const 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(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if(ok) return g;
}
}
constexpr int countr_zero(const unsigned int n) {
int res = 0;
while(!(n & (1 << res))) ++res;
return res;
}
template <typename mint, int g = primitive_root(mint::mod())>
struct FFT_Info {
static constexpr int rank2 = countr_zero(mint::mod() - 1);
array<mint, rank2 + 1> root;
array<mint, rank2 + 1> iroot;
array<mint, max(0, rank2 - 2 + 1)> rate2;
array<mint, max(0, rank2 - 2 + 1)> irate2;
array<mint, max(0, rank2 - 3 + 1)> rate3;
array<mint, 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 <typename mint>
void butterfly(vector<mint>& a) {
const int n = (int)a.size();
const int h = __builtin_ctz((unsigned int)n);
static const FFT_Info<mint> info;
int len = 0;
while(len < h) {
if(h - len == 1) {
const int p = 1 << (h - len - 1);
mint rot = 1;
for(int s = 0; s < (1 << len); ++s) {
const int offset = s << (h - len);
for(int i = 0; i < p; ++i) {
const auto l = a[i + offset];
const 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[__builtin_ctz(~(unsigned int)(s))];
}
++len;
} else {
const int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for(int s = 0; s < (1 << len); ++s) {
const mint rot2 = rot * rot;
const mint rot3 = rot2 * rot;
const int offset = s << (h - len);
for(int i = 0; i < p; ++i) {
const auto mod2 = 1ULL * mint::mod() * mint::mod();
const auto a0 = 1ULL * a[i + offset].val();
const auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
const auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
const auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
const auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
const 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[__builtin_ctz(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <typename mint>
void butterfly_inv(vector<mint>& a) {
const int n = (int)a.size();
const int h = __builtin_ctz((unsigned int)n);
static const FFT_Info<mint> info;
int len = h;
while(len) {
if(len == 1) {
const int p = 1 << (h - len);
mint irot = 1;
for(int s = 0; s < (1 << (len - 1)); ++s) {
const int offset = s << (h - len + 1);
for(int i = 0; i < p; ++i) {
const auto l = a[i + offset];
const 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[__builtin_ctz(~(unsigned int)(s))];
}
--len;
} else {
const int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for(int s = 0; s < (1 << (len - 2)); ++s) {
const mint irot2 = irot * irot;
const mint irot3 = irot2 * irot;
const int offset = s << (h - len + 2);
for(int i = 0; i < p; ++i) {
const auto a0 = 1ULL * a[i + offset + 0 * p].val();
const auto a1 = 1ULL * a[i + offset + 1 * p].val();
const auto a2 = 1ULL * a[i + offset + 2 * p].val();
const auto a3 = 1ULL * a[i + offset + 3 * p].val();
const 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[__builtin_ctz(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <typename mint>
vector<mint> convolution_naive(const vector<mint>& a, const vector<mint>& b) {
const int n = (int)a.size(), m = (int)b.size();
vector<mint> res(n + m - 1);
if(n < m) {
for(int j = 0; j < m; ++j) {
for(int i = 0; i < n; ++i) {
res[i + j] += a[i] * b[j];
}
}
} else {
for(int i = 0; i < n; ++i) {
for(int j = 0; j < m; ++j) {
res[i + j] += a[i] * b[j];
}
}
}
return res;
}
template <typename mint>
vector<mint> convolution(vector<mint> a, vector<mint> b) {
const int n = (int)a.size(), m = (int)b.size();
if(n == 0 or m == 0) return {};
int z = 1;
while(z < n + m - 1) z *= 2;
assert((mint::mod() - 1) % z == 0);
if(min(n, m) <= 60) return convolution_naive(a, b);
a.resize(z);
b.resize(z);
butterfly(a);
butterfly(b);
for(int i = 0; i < z; ++i) a[i] *= b[i];
butterfly_inv(a);
a.resize(n + m - 1);
const mint iz = mint(z).inv();
for(int i = 0; i < n + m - 1; ++i) a[i] *= iz;
return a;
}
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using F = FormalPowerSeries;
F& operator=(const vector<mint>& g) {
const int n = (*this).size();
const int m = g.size();
if(n < m) (*this).resize(m);
for(int i = 0; i < m; ++i) (*this)[i] = g[i];
return (*this);
}
F& operator-() {
const int n = (*this).size();
for(int i = 0; i < n; ++i) (*this)[i] *= -1;
return (*this);
}
F& operator+=(const F& g) {
const int n = (*this).size();
const int m = g.size();
if(n < m) (*this).resize(m);
for(int i = 0; i < m; ++i) (*this)[i] += g[i];
return (*this);
}
F& operator+=(const mint& r) {
if((*this).empty()) (*this).resize(1, mint(0));
(*this)[0] += r;
return (*this);
}
F& operator-=(const F& g) {
const int n = (*this).size();
const int m = g.size();
if(n < m) (*this).resize(m);
for(int i = 0; i < m; ++i) (*this)[i] -= g[i];
return (*this);
}
F& operator-=(const mint& r) {
if((*this).empty()) (*this).resize(1, mint(0));
(*this)[0] -= r;
return (*this);
}
F& operator*=(const F& g) {
(*this) = convolution((*this), g);
return (*this);
}
F& operator*=(const mint& r) {
const int n = (*this).size();
for(int i = 0; i < n; ++i) (*this)[i] *= r;
return (*this);
}
F& operator/=(const F& g) {
if((*this).size() < g.size()) {
(*this).clear();
return (*this);
}
const int n = (*this).size() - g.size() + 1;
(*this) = ((*this).rev().pre(n) * g.rev().inv(n)).pre(n).rev();
return (*this);
}
F& operator/=(const mint& r) {
const int n = (*this).size();
const mint inv_r = r.inv();
for(int i = 0; i < n; ++i) (*this)[i] *= inv_r;
return (*this);
}
F& operator%=(const F& g) {
(*this) -= (*this) / g * g;
shrink();
return (*this);
}
F operator*(const mint& g) const {
return F(*this) *= g;
}
F operator-(const mint& g) const {
return F(*this) -= g;
}
F operator+(const mint& g) const {
return F(*this) += g;
}
F operator/(const mint& g) const {
return F(*this) /= g;
}
F operator*(const F& g) const {
return F(*this) *= g;
}
F operator-(const F& g) const {
return F(*this) -= g;
}
F operator+(const F& g) const {
return F(*this) += g;
}
F operator/(const F& g) const {
return F(*this) /= g;
}
F operator%(const F& g) const {
return F(*this) %= g;
}
F operator<<(const int d) const {
F ret(*this);
ret.insert(ret.begin(), d, mint(0));
return ret;
}
F operator>>(const int d) const {
const int n = (*this).size();
if(n <= d) return {};
F ret(*this);
ret.erase(ret.begin(), ret.begin() + d);
return ret;
}
void shrink() {
while(!(*this).empty() and (*this).back() == mint(0)) (*this).pop_back();
}
F rev() const {
F ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
F pre(const int deg) const {
assert(deg >= 0);
F ret(begin(*this), begin(*this) + min((int)(*this).size(), deg));
if((int)ret.size() < deg) ret.resize(deg);
return ret;
}
mint eval(const mint& a) const {
const int n = (*this).size();
mint x = 1, ret = 0;
for(int i = 0; i < n; ++i) {
ret += (*this)[i] * x;
x *= a;
}
return ret;
}
void onemul(const int d, const mint& c, int deg = -1) {
assert(deg >= -1);
const int n = (*this).size();
if(deg == -1) deg = n + d;
if(deg > n) (*this).resize(deg);
for(int i = deg - d - 1; i >= 0; --i) {
(*this)[i + d] += (*this)[i] * c;
}
}
void onediv(const int d, const mint& c, int deg = -1) {
assert(deg >= -1);
const int n = (*this).size();
if(deg == -1) deg = n;
if(deg > n) (*this).resize(deg + 1);
for(int i = 0; i < deg - d; ++i) {
(*this)[i + d] -= (*this)[i] * c;
}
}
F diff() const {
const int n = (*this).size();
F ret(max(0, n - 1));
for(int i = 1; i < n; ++i) ret[i - 1] = (*this)[i] * i;
return ret;
}
F integral() const {
const int n = (*this).size();
static constexpr int mod = mint::mod();
F ret(n + 1);
ret[0] = mint(0);
if(n > 0) ret[1] = mint(1);
for(int i = 2; i <= n; ++i) ret[i] = (-ret[mod % i]) * (mod / i);
for(int i = 0; i < n; ++i) ret[i + 1] *= (*this)[i];
return ret;
}
F inv(int deg = -1) const {
assert(deg >= -1);
const int n = (*this).size();
assert(n > 0 and (*this)[0] != mint(0));
if(deg == -1) deg = n;
F g(1);
g[0] = (*this)[0].inv();
while((int)g.size() < deg) {
const int m = g.size();
F f(begin(*this), begin(*this) + min(n, 2 * m));
F r(g);
f.resize(2 * m);
r.resize(2 * m);
butterfly(f);
butterfly(r);
for(int i = 0; i < 2 * m; ++i) f[i] *= r[i];
butterfly_inv(f);
f.erase(f.begin(), f.begin() + m);
f.resize(2 * m);
butterfly(f);
for(int i = 0; i < 2 * m; ++i) f[i] *= r[i];
butterfly_inv(f);
mint in = mint(2 * m).inv();
in *= -in;
for(int i = 0; i < m; ++i) f[i] *= in;
g.insert(g.end(), f.begin(), f.begin() + m);
}
return g.pre(deg);
}
F log(int deg = -1) const {
assert(deg >= -1);
const int n = (*this).size();
assert(n > 0 and (*this)[0] == mint(1));
if(deg == -1) deg = n;
return ((*this).diff() * (*this).inv(deg)).pre(deg - 1).integral();
}
F exp(int deg = -1) const {
assert(deg >= -1);
const int n = (*this).size();
assert(n == 0 or (*this)[0] == 0);
if(deg == -1) deg = n;
F Inv;
Inv.reserve(deg + 1);
Inv.emplace_back(mint(0));
Inv.emplace_back(mint(1));
auto inplace_integral = [&](F& f) -> void {
const int n = (int)f.size();
static constexpr int mod = mint::mod();
while((int)Inv.size() <= n) {
const int i = Inv.size();
Inv.emplace_back((-Inv[mod % i]) * (mod / i));
}
f.insert(begin(f), mint(0));
for(int i = 1; i <= n; ++i) f[i] *= Inv[i];
};
auto inplace_diff = [](F& f) -> void {
if(f.empty()) return;
f.erase(begin(f));
mint coeff = 1;
for(int i = 0; i < (int)f.size(); ++i) {
f[i] *= coeff;
++coeff;
}
};
F b{1, 1 < (int)(*this).size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for(int m = 2; m < deg; m <<= 1) {
auto y = b;
y.resize(2 * m);
butterfly(y);
z1 = z2;
F z(m);
for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
butterfly_inv(z);
const mint si = mint(m).inv();
for(int i = 0; i < m; ++i) z[i] *= si;
fill(begin(z), begin(z) + m / 2, mint(0));
butterfly(z);
for(int i = 0; i < m; ++i) z[i] *= -z1[i];
butterfly_inv(z);
for(int i = 0; i < m; ++i) z[i] *= si;
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
butterfly(z2);
F x(begin((*this)), begin((*this)) + min<int>((*this).size(), m));
x.resize(m);
inplace_diff(x);
x.emplace_back(mint(0));
butterfly(x);
for(int i = 0; i < m; ++i) x[i] *= y[i];
butterfly_inv(x);
for(int i = 0; i < m; ++i) x[i] *= si;
x -= b.diff();
x.resize(2 * m);
for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
butterfly(x);
for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
butterfly_inv(x);
const mint si2 = mint(m << 1).inv();
for(int i = 0; i < 2 * m; ++i) x[i] *= si2;
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, mint(0));
butterfly(x);
for(int i = 0; i < 2 * m; ++i) x[i] *= y[i];
butterfly_inv(x);
for(int i = 0; i < 2 * m; ++i) x[i] *= si2;
b.insert(end(b), begin(x) + m, end(x));
}
return b.pre(deg);
}
F pow(const long long k, int deg = -1) const {
assert(deg >= -1);
assert(k >= 0);
const int n = (*this).size();
if(deg == -1) deg = n;
if(k == 0) {
F ret(deg);
if(deg) ret[0] = 1;
return ret;
}
for(int i = 0; i < n; ++i) {
if((*this)[i] != mint(0)) {
const mint rev = mint(1) / (*this)[i];
F ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(deg);
if((int)ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
if(__int128_t(i + 1) * k >= deg) return F(deg, mint(0));
}
return F(deg, mint(0));
}
F shift(const mint& c) const {
const int n = (*this).size();
vector<mint> fact(n), ifact(n);
fact[0] = ifact[0] = mint(1);
for(int i = 1; i < n; ++i) fact[i] = fact[i - 1] * i;
ifact[n - 1] = mint(1) / fact[n - 1];
for(int i = n - 1; i > 1; --i) ifact[i - 1] = ifact[i] * i;
F ret(*this);
for(int i = 0; i < n; ++i) ret[i] *= fact[i];
ret = ret.rev();
F bs(n, mint(1));
for(int i = 1; i < n; ++i) bs[i] = bs[i - 1] * c * ifact[i] * fact[i - 1];
ret = (ret * bs).pre(n);
ret = ret.rev();
for(int i = 0; i < n; ++i) ret[i] *= ifact[i];
return ret;
}
};
using fps = FormalPowerSeries<mint>;
template <template <typename> typename FPS, typename mint>
FPS<mint> berlekamp_massey(const FPS<mint>& s) {
const int n = (int)s.size();
FPS<mint> b = {mint(-1)}, c = {mint(-1)};
mint y = mint(1);
for(int ed = 1; ed <= n; ++ed) {
int l = (int)c.size(), m = (int)b.size();
mint x = 0;
for(int i = 0; i < l; ++i) x += c[i] * s[ed - l + i];
b.emplace_back(0);
++m;
if(x == mint(0)) continue;
const mint freq = x / y;
if(l < m) {
const auto tmp = c;
c.insert(begin(c), m - l, mint(0));
for(int i = 0; i < m; ++i) c[m - 1 - i] -= freq * b[m - 1 - i];
b = tmp;
y = x;
} else {
for(int i = 0; i < m; ++i) c[l - 1 - i] -= freq * b[m - 1 - i];
}
}
c.pop_back();
c = c.rev();
return c;
}
template <template <typename> typename FPS, typename mint>
mint bostan_mori(const FPS<mint>& a, const FPS<mint>& c, long long k) {
assert(k >= 0);
if(k < (int)a.size()) return a[k];
assert(a.size() >= c.size());
FPS<mint> q = FPS<mint>{1} - (c << 1);
FPS<mint> p = (a * q).pre((int)c.size());
if(p.empty()) return 0;
while(k > 0) {
auto q2 = q;
for(int i = 1; i < (int)q2.size(); i += 2) q2[i] = -q2[i];
const auto s = p * q2;
const auto t = q * q2;
if(k & 1) {
for(int i = 1; i < (int)s.size(); i += 2) p[i >> 1] = s[i];
for(int i = 0; i < (int)t.size(); i += 2) q[i >> 1] = t[i];
} else {
for(int i = 0; i < (int)s.size(); i += 2) p[i >> 1] = s[i];
for(int i = 0; i < (int)t.size(); i += 2) q[i >> 1] = t[i];
}
k >>= 1;
}
return p[0];
}
template <template <typename> typename FPS, typename mint>
mint nth_term(const FPS<mint>& s, const long long n) {
assert(n >= 0);
const FPS<mint> c = berlekamp_massey(s);
return bostan_mori(s, c, n);
}
int main(void) {
ll n, k;
cin >> n >> k;
vector<mint> f(1000000);
f[1] = 1, f[2] = 1;
rep(i, 3, 1000000) f[i] = f[i - 1] + f[i - 2];
fps s(1000000);
rep(i, 1, 1000000) {
s[i] = s[i - 1] + f[i].pow(k);
}
cout << nth_term(s, n) << '\n';
}