結果
| 問題 | No.1559 Next Rational |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2021-06-26 00:33:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 34,088 bytes |
| コンパイル時間 | 4,062 ms |
| コンパイル使用メモリ | 248,272 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-06-25 09:01:26 |
| 合計ジャッジ時間 | 5,221 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,816 KB |
| testcase_02 | AC | 2 ms
6,816 KB |
| testcase_03 | RE | - |
| testcase_04 | RE | - |
| testcase_05 | AC | 2 ms
6,944 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 2 ms
6,940 KB |
| testcase_08 | AC | 3 ms
6,944 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | RE | - |
| testcase_11 | RE | - |
| testcase_12 | AC | 2 ms
6,944 KB |
| testcase_13 | AC | 2 ms
6,940 KB |
| testcase_14 | AC | 2 ms
6,940 KB |
| testcase_15 | AC | 2 ms
6,944 KB |
| testcase_16 | AC | 2 ms
6,944 KB |
| testcase_17 | AC | 2 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h>
#pragma region Header
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v)
{
return v;
}
constexpr i32 operator"" _u32(u64 v)
{
return v;
}
constexpr i64 operator"" _i64(u64 v)
{
return v;
}
constexpr u64 operator"" _u64(u64 v)
{
return v;
}
constexpr f64 operator"" _f64(f80 v)
{
return v;
}
constexpr f80 operator"" _f80(f80 v)
{
return v;
}
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<typename T>
using IList = std::initializer_list<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
using NSec = std::chrono::nanoseconds;
using USec = std::chrono::microseconds;
using MSec = std::chrono::milliseconds;
using Sec = std::chrono::seconds;
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(const int n)
{
return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
Ostream& operator<<(Ostream& os, i128 v)
{
bool minus = false;
if (v < 0) { minus = true, v = -v; }
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << (minus ? "-" : "") << ans;
}
Ostream& operator<<(Ostream& os, u128 v)
{
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << ans;
}
template<typename T>
bool chmin(T& a, const T& b)
{
if (a > b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
bool chmax(T& a, const T& b)
{
if (a < b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
constexpr T fdiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T cdiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T modPower(T v, I n, T mod)
{
T ans = 1 % mod;
for (; n > 0; n >>= 1, (v *= v) %= mod) {
if (n % 2 == 1) { (ans *= v) %= mod; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n)
{
T ans = 1;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n, const T& e)
{
T ans = e;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T>
Vec<T> operator+=(Vec<T>& vs1, const Vec<T>& vs2)
{
vs1.insert(vs1.end(), vs2.begin(), vs2.end());
return vs1;
}
template<typename T>
Vec<T> operator+(const Vec<T>& vs1, const Vec<T>& vs2)
{
auto vs = vs1;
vs += vs2;
return vs;
}
template<typename T>
void fillAll(Vec<T>& vs, const T& v)
{
std::fill(vs.begin(), vs.end(), v);
}
template<typename T, typename C = Lt<T>>
void sortAll(Vec<T>& vs, C comp = C{})
{
std::sort(vs.begin(), vs.end(), comp);
}
template<typename T>
void reverseAll(Vec<T>& vs)
{
std::reverse(vs.begin(), vs.end());
}
template<typename T>
void uniqueAll(Vec<T>& vs)
{
sortAll(vs);
vs.erase(std::unique(vs.begin(), vs.end()), vs.end());
}
template<typename T, typename V = T>
V sumAll(const Vec<T>& vs)
{
return std::accumulate(vs.begin(), vs.end(), V{});
}
template<typename T>
int minInd(const Vec<T>& vs)
{
return std::min_element(vs.begin(), vs.end()) - vs.begin();
}
template<typename T>
int maxInd(const Vec<T>& vs)
{
return std::max_element(vs.begin(), vs.end()) - vs.begin();
}
template<typename T>
int lbInd(const Vec<T>& vs, const T& v)
{
return std::lower_bound(vs.begin(), vs.end(), v) - vs.begin();
}
template<typename T>
int ubInd(const Vec<T>& vs, const T& v)
{
return std::upper_bound(vs.begin(), vs.end(), v) - vs.begin();
}
template<typename T, typename F>
Vec<T> genVec(int n, F gen)
{
Vec<T> ans;
std::generate_n(std::back_insert_iterator(ans), n, gen);
return ans;
}
Vec<int> iotaVec(int n, int offset = 0)
{
Vec<int> ans(n);
std::iota(ans.begin(), ans.end(), offset);
return ans;
}
template<typename T>
Vec<T> revVec(const Vec<T>& vs)
{
auto ans = vs;
reverseAll(ans);
return ans;
}
constexpr int popcount(const u64 v)
{
return v ? __builtin_popcountll(v) : 0;
}
constexpr int log2p1(const u64 v)
{
return v ? 64 - __builtin_clzll(v) : 0;
}
constexpr int lsbp1(const u64 v)
{
return __builtin_ffsll(v);
}
constexpr int clog(const u64 v)
{
return v ? log2p1(v - 1) : 0;
}
constexpr u64 ceil2(const u64 v)
{
const int l = clog(v);
return (l == 64) ? 0_u64 : (1_u64 << l);
}
constexpr u64 floor2(const u64 v)
{
return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64;
}
constexpr bool ispow2(const u64 v)
{
return (v > 0) and ((v & (v - 1)) == 0);
}
constexpr bool btest(const u64 mask, const int ind)
{
return (mask >> ind) & 1_u64;
}
template<typename F>
struct Fix : F
{
Fix(F&& f) : F{std::forward<F>(f)} {}
template<typename... Args>
auto operator()(Args&&... args) const
{
return F::operator()(*this, std::forward<Args>(args)...);
}
};
class irange
{
private:
struct itr
{
itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
bool operator!=(const itr& it) const
{
return m_cnt != it.m_cnt;
}
int operator*()
{
return m_cnt;
}
itr& operator++()
{
m_cnt += m_step;
return *this;
}
i64 m_cnt, m_step;
};
i64 m_start, m_end, m_step;
public:
irange(i64 start, i64 end, i64 step = 1)
{
assert(step != 0);
const i64 d = std::abs(step);
const i64 l = (step > 0 ? start : end);
const i64 r = (step > 0 ? end : start);
int n = (r - l) / d + ((r - l) % d ? 1 : 0);
if (l >= r) { n = 0; }
m_start = start;
m_end = start + step * n;
m_step = step;
}
itr begin() const
{
return itr{m_start, m_step};
}
itr end() const
{
return itr{m_end, m_step};
}
};
irange rep(int end)
{
return irange(0, end, 1);
}
irange per(int rend)
{
return irange(rend - 1, -1, -1);
}
#pragma COMMENT("[REFS] Xoshiro: https://prng.di.unimi.it")
namespace xoshiro_impl {
u64 x;
u64 next()
{
uint64_t z = (x += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
return z ^ (z >> 31);
}
}
class Xoshiro32
{
public:
using result_type = u32;
using T = result_type;
Xoshiro32(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (32 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 9;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 11);
return ans;
}
T s[4];
};
class Xoshiro64
{
public:
using result_type = u64;
using T = result_type;
Xoshiro64(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (64 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 45);
return ans;
}
T s[4];
};
template<typename Rng>
class RNG
{
public:
using result_type = typename Rng::result_type;
using T = result_type;
static constexpr T min()
{
return Rng::min();
}
static constexpr T max()
{
return Rng::max();
}
RNG() : RNG(std::random_device{}()) {}
RNG(T seed) : m_rng(seed) {}
T operator()()
{
return m_rng();
}
template<typename T>
T val(T min, T max)
{
return std::uniform_int_distribution<T>(min, max)(m_rng);
}
template<typename T>
Pair<T, T> pair(T min, T max)
{
return std::minmax({val<T>(min, max), val<T>(min, max)});
}
template<typename T>
Vec<T> vec(int n, T min, T max)
{
return genVec<T>(n, [&]() { return val<T>(min, max); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, T min, T max)
{
return genVec<Vec<T>>(n, [&]() { return vec(m, min, max); });
}
private:
Rng m_rng;
};
RNG<std::mt19937> rng;
RNG<std::mt19937_64> rng64;
RNG<Xoshiro32> rng_xo;
RNG<Xoshiro64> rng_xo64;
class Scanner
{
public:
Scanner(Istream& is = std::cin) : m_is{is}
{
m_is.tie(nullptr)->sync_with_stdio(false);
}
template<typename T>
T val()
{
T v;
return m_is >> v, v;
}
template<typename T>
T val(T offset)
{
return val<T>() - offset;
}
template<typename T>
Vec<T> vec(int n)
{
return genVec<T>(n, [&]() { return val<T>(); });
}
template<typename T>
Vec<T> vec(int n, T offset)
{
return genVec<T>(n, [&]() { return val<T>(offset); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, const T offset)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
}
template<typename... Args>
auto tup()
{
return Tup<Args...>{val<Args>()...};
}
template<typename... Args>
auto tup(const Args&... offsets)
{
return Tup<Args...>{val<Args>(offsets)...};
}
private:
Istream& m_is;
};
Scanner in;
class Printer
{
public:
Printer(Ostream& os = std::cout) : m_os{os}
{
m_os << std::fixed << std::setprecision(15);
}
template<typename... Args>
int operator()(const Args&... args)
{
dump(args...);
return 0;
}
template<typename... Args>
int ln(const Args&... args)
{
dump(args...), m_os << '\n';
return 0;
}
template<typename... Args>
int el(const Args&... args)
{
dump(args...), m_os << std::endl;
return 0;
}
private:
template<typename T>
void dump(const T& v)
{
m_os << v;
}
template<typename T>
void dump(const Vec<T>& vs)
{
for (const int i : rep(vs.size())) {
m_os << (i ? " " : ""), dump(vs[i]);
}
}
template<typename T>
void dump(const Vec<Vec<T>>& vss)
{
for (const int i : rep(vss.size())) {
m_os << (i ? "\n" : ""), dump(vss[i]);
}
}
template<typename T, typename... Ts>
int dump(const T& v, const Ts&... args)
{
dump(v), m_os << ' ', dump(args...);
return 0;
}
Ostream& m_os;
};
Printer out;
template<typename T, int n, int i = 0>
auto ndVec(int const (&szs)[n], const T x = T{})
{
if constexpr (i == n) {
return x;
} else {
return std::vector(szs[i], ndVec<T, n, i + 1>(szs, x));
}
}
template<typename T, typename F>
T binSearch(T ng, T ok, F check)
{
while (std::abs(ok - ng) > 1) {
const T mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template<u32 mod_, u32 root_, u32 max2p_>
class modint
{
template<typename U = u32&>
static U modRef()
{
static u32 s_mod = 0;
return s_mod;
}
template<typename U = u32&>
static U rootRef()
{
static u32 s_root = 0;
return s_root;
}
template<typename U = u32&>
static U max2pRef()
{
static u32 s_max2p = 0;
return s_max2p;
}
public:
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u32>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
modRef() = m;
}
template<typename U = u32>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u32>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint() : m_val{0} {}
constexpr modint(i64 v) : m_val{normll(v)} {}
constexpr void setRaw(u32 v)
{
m_val = v;
}
constexpr modint operator-() const
{
return modint{0} - (*this);
}
constexpr modint& operator+=(const modint& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint& operator-=(const modint& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint& operator*=(const modint& m)
{
m_val = normll((i64)m_val * (i64)m.val() % (i64)mod());
return *this;
}
constexpr modint& operator/=(const modint& m)
{
return *this *= m.inv();
}
constexpr modint operator+(const modint& m) const
{
auto v = *this;
return v += m;
}
constexpr modint operator-(const modint& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint operator*(const modint& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint operator/(const modint& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint& m) const
{
return m_val == m.val();
}
constexpr bool operator!=(const modint& m) const
{
return not(*this == m);
}
friend Istream& operator>>(Istream& is, modint& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint& m)
{
return os << m.val();
}
constexpr u32 val() const
{
return m_val;
}
template<typename I>
constexpr modint pow(I n) const
{
return power(*this, n);
}
constexpr modint inv() const
{
return pow(mod() - 2);
}
static modint sinv(u32 n)
{
static Vec<modint> is{1, 1};
for (u32 i = (u32)is.size(); i <= n; i++) {
is.push_back(-is[mod() % i] * (mod() / i));
}
return is[n];
}
static modint fact(u32 n)
{
static Vec<modint> fs{1, 1};
for (u32 i = (u32)fs.size(); i <= n; i++) {
fs.push_back(fs.back() * i);
}
return fs[n];
}
static modint ifact(u32 n)
{
static Vec<modint> ifs{1, 1};
for (u32 i = (u32)ifs.size(); i <= n; i++) {
ifs.push_back(ifs.back() * sinv(i));
}
return ifs[n];
}
static modint comb(int n, int k)
{
return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static constexpr u32 norm(u32 x)
{
return x < mod() ? x : x - mod();
}
static constexpr u32 normll(i64 x)
{
return norm(u32(x % (i64)mod() + (i64)mod()));
}
u32 m_val;
};
using modint_1000000007 = modint<1000000007, 5, 1>;
using modint_998244353 = modint<998244353, 3, 23>;
template<int id>
using modint_dynamic = modint<0, 0, id>;
template<typename T>
Vec<T> berlekampMassey(const Vec<T>& A)
{
const int N = (int)A.size();
Vec<T> B{1}, C{1};
T b = 1;
for (int j : irange(1, N + 1)) {
int m = (int)B.size(), l = (int)C.size();
T d = 0;
for (int i : rep(l)) {
d += A[j - l + i] * C[i];
}
B.push_back(0), m++;
if (d == 0) { continue; }
const T c = -d / b;
if (l < m) {
auto temp = C;
C.insert(C.begin(), m - l, 0);
for (int i : rep(m)) {
C[m - 1 - i] += c * B[m - 1 - i];
}
B = temp, b = d;
} else {
for (int i : rep(m)) {
C[l - 1 - i] += c * B[m - 1 - i];
}
}
}
reverseAll(C);
return C;
}
template<typename mint>
class FPS : public Vec<mint>
{
public:
using std::vector<mint>::vector;
using std::vector<mint>::resize;
FPS(const Vec<mint>& vs) : Vec<mint>{vs} {}
int size() const
{
return Vec<mint>::size();
}
int deg() const
{
return size() - 1;
}
FPS low(int n) const
{
return FPS{this->begin(), this->begin() + std::min(n, size())};
}
FPS rev() const
{
FPS ans = *this;
reverseAll(ans);
return ans;
}
mint eval(const mint& x) const
{
mint ans = 0;
mint power = 1;
for (int i : rep(size())) {
ans += power * (*this)[i];
power *= x;
}
return ans;
}
mint& operator[](const int n)
{
if (deg() < n) { resize(n + 1); }
return Vec<mint>::operator[](n);
}
const mint& operator[](const int n) const
{
return Vec<mint>::operator[](n);
}
mint at(const int n) const
{
return (n < size() ? (*this)[n] : mint{0});
}
FPS operator-() const
{
FPS ans = *this;
for (auto& v : ans) {
v = -v;
}
return ans;
}
FPS& operator+=(const FPS& f)
{
for (int i : rep(f.size())) {
(*this)[i] += f[i];
}
return *this;
}
FPS& operator-=(const FPS& f)
{
for (int i : rep(f.size())) {
(*this)[i] -= f[i];
}
return *this;
}
FPS& operator*=(const FPS& f)
{
return (*this) = (*this) * f;
}
FPS& operator<<=(const int s)
{
return *this = (*this << s);
}
FPS& operator>>=(const int s)
{
return *this = (*this >> s);
}
FPS operator+(const FPS& f) const
{
return FPS(*this) += f;
}
FPS operator-(const FPS& f) const
{
return FPS(*this) -= f;
}
FPS operator*(const FPS& f) const
{
return mult(f, size() + f.size() - 1);
}
FPS operator<<(const int s) const
{
FPS ans(size() + s);
for (int i : rep(size())) {
ans[i + s] = (*this)[i];
}
return ans;
}
FPS operator>>(const int s) const
{
FPS ans;
for (int i : irange(s, size())) {
ans[i - s] = (*this)[i];
}
return ans;
}
friend Ostream& operator<<(Ostream& os, const FPS& f)
{
return os << static_cast<Vec<mint>>(f);
}
FPS derivative() const
{
FPS ans;
for (int i : irange(1, size())) {
ans[i - 1] = (*this)[i] * i;
}
return ans;
}
FPS integral() const
{
FPS ans;
for (int i : irange(1, size() + 1)) {
ans[i] = (*this)[i - 1] * mint::sinv(i);
}
return ans;
}
FPS mult(const FPS& f, int sz) const
{
if (sz == 0) { return FPS{}; }
const int N = std::min(size(), sz) + std::min(f.size(), sz) - 1;
if (N < 10) {
FPS ans;
for (int i : rep(sz)) {
for (int j : rep(sz)) {
if (i + j >= sz) { break; }
ans[i + j] += this->at(i) * f.at(j);
}
}
return ans;
}
if (N <= (1 << mint::max2p())) {
auto ans = conv<mint>(*this, f, sz);
return ans;
} else {
const auto cs1 = conv<submint1>(*this, f, sz);
const auto cs2 = conv<submint2>(*this, f, sz);
const auto cs3 = conv<submint3>(*this, f, sz);
FPS ans((int)cs1.size());
for (int i : rep(cs1.size())) {
ans[i] = restore(cs1[i].val(), cs2[i].val(), cs3[i].val());
}
return ans;
}
}
FPS smult(int p, const mint a, int sz)
{
FPS ans = low(sz);
for (int i = 0; i + p < sz; i++) {
ans[i + p] += (*this)[i] * a;
}
return ans;
}
FPS sdiv(int p, const mint& a, int sz)
{
FPS ans = low(sz);
for (int i = 0; i + p < sz; i++) {
ans[i + p] -= ans[i] * a;
}
return ans;
}
FPS inv(int sz) const
{
const int n = size();
assert((*this)[0].val() != 0);
const int N = n * 2 - 1;
if (N <= (1 << mint::max2p())) {
FPS r{(*this)[0].inv()};
for (int lg = 0, m = 1; m < sz; m <<= 1, lg++) {
FPS f{this->begin(), this->begin() + std::min(n, 2 * m)};
FPS g = r;
f.resize(2 * m), g.resize(2 * m);
trans(f, lg + 1, false), trans(g, lg + 1, false);
for (int i : rep(2 * m)) {
f[i] *= g[i];
}
trans(f, lg + 1, true);
std::fill(f.begin(), f.begin() + m, 0);
trans(f, lg + 1, false);
for (int i : rep(2 * m)) {
f[i] *= g[i];
}
trans(f, lg + 1, true);
for (int i = m; i < std::min(2 * m, sz); i++) {
r[i] = -f[i];
}
}
return r;
} else {
FPS g{(*this)[0].inv()};
for (int lg = 0, m = 1; m < sz; m <<= 1, lg++) {
g = FPS{2} * g - this->mult(g.mult(g, 2 * m), 2 * m);
}
return g.low(sz);
}
}
FPS log(const int sz) const
{
assert((*this)[0].val() == 1);
auto ans = derivative().mult(inv(sz), sz).integral();
ans.resize(sz);
return ans;
}
FPS exp(const int sz) const
{
const int l = lsb(sz);
if (l == -1) { return FPS{1}.low(sz); }
assert((*this)[0].val() == 0);
const int n = size();
const int N = n * 2 - 1;
if (N <= (1 << mint::max2p())) {
FPS f = {1, (*this)[1]}, g{1}, G{1, 1};
for (int m = 2, lg = 1; m < sz; m <<= 1, lg++) {
auto F = f;
F.resize(2 * m), trans(F, lg + 1, false);
FPS z(m);
for (int i : rep(m)) {
z[i] = F[i] * G[i];
}
trans(z, lg, true);
std::fill(z.begin(), z.begin() + m / 2, 0);
trans(z, lg, false);
for (int i : rep(m)) {
z[i] *= G[i];
}
trans(z, lg, true);
for (int i : irange(m / 2, m)) {
g[i] = -z[i];
}
G = g, G.resize(m * 2), trans(G, lg + 1, false);
auto q = low(m).derivative();
q.resize(m), trans(q, lg, false);
for (int i : rep(m)) {
q[i] *= F[i];
}
trans(q, lg, true);
const auto df = f.derivative();
for (int i : rep(m - 1)) {
q[i] -= df[i];
}
q.resize(m * 2);
for (int i : rep(m - 1)) {
q[m + i] = q[i], q[i] = 0;
}
trans(q, lg + 1, false);
for (int i : rep(m * 2)) {
q[i] *= G[i];
}
trans(q, lg + 1, true);
q.pop_back();
q = q.integral();
for (int i = m; i < std::min(size(), m * 2); i++) {
q[i] += (*this)[i];
}
std::fill(q.begin(), q.begin() + m, 0);
trans(q, lg + 1, false);
for (int i = 0; i < m * 2; i++) {
q[i] *= F[i];
}
trans(q, lg + 1, true);
for (int i = m; i < 2 * m; i++) {
f[i] = q[i];
}
}
return f.low(sz);
} else {
FPS f{1};
for (int m = 1; m < sz; m <<= 1) {
auto g = low(2 * m);
g[0] += 1;
f.resize(2 * m);
g -= f.log(2 * m);
g = f.mult(g, 2 * m);
for (int i = m; i < std::min(2 * m, g.size()); i++) {
f[i] = g[i];
}
}
return f.low(sz);
}
}
template<typename I>
FPS pow(I n) const
{
return pow(n, deg() * n + 1);
}
template<typename I>
FPS pow(I n, int sz) const
{
if (n == 0) { return FPS{1}.low(sz); }
if (size() == 0) { return FPS{}; }
const int p = lsb(deg() / n);
if (p == -1) { return FPS{}; }
const mint a = (*this)[p];
FPS f = (*this) >> p;
for (auto& c : f) {
c /= a;
}
f = f.log(sz - p * n);
for (auto& c : f) {
c *= n;
}
f = f.exp(sz - p * n);
FPS g;
for (int i : rep(f.size())) {
g[i + p * n] = f[i] * a.pow(n);
}
return g;
}
FPS tshift(const mint& c) const
{
const int N = size();
FPS f(N), d(N);
for (int i = 0; i < N; i++) {
d[i] = c.pow(N - 1 - i) * mint::ifact(N - 1 - i);
}
for (int i = 0; i < N; i++) {
f[i] = (*this)[i] * mint::fact(i);
}
f = f * d;
FPS g(N);
for (int i = 0; i < N; i++) {
g[i] = f[i + N - 1] * mint::ifact(i);
}
return g;
}
FPS quot(const FPS& g) const
{
const int N = size(), M = g.size();
if (N < M) { return FPS{}; }
const auto fR = rev(), gR = g.rev();
return fR.mult(gR.inv(N - M + 1), N - M + 1).rev();
}
FPS rem(const FPS& g) const
{
return (*this) - g * quot(g);
}
private:
int lsb() const
{
return lsb(deg());
}
int lsb(int sz) const
{
for (int p : rep(sz + 1)) {
if ((*this)[p].val() != 0) { return p; }
}
return -1;
}
using submint1 = modint<469762049, 3, 26>;
using submint2 = modint<167772161, 3, 25>;
using submint3 = modint<754974721, 11, 24>;
template<typename submint>
static void trans(Vec<submint>& as, int lg, bool rev)
{
const int N = 1 << lg;
assert((int)as.size() == N);
Vec<submint> rs, irs;
if (rs.empty()) {
const submint r = submint(submint::root()), ir = r.inv();
rs.resize(submint::max2p() + 1), irs.resize(submint::max2p() + 1);
rs.back() = -r.pow((submint::mod() - 1) >> submint::max2p()),
irs.back() = -ir.pow((submint::mod() - 1) >> submint::max2p());
for (u32 i : irange(submint::max2p(), 0, -1)) {
rs[i - 1] = -(rs[i] * rs[i]);
irs[i - 1] = -(irs[i] * irs[i]);
}
}
const auto drange = (rev ? irange(0, lg, 1) : irange(lg - 1, -1, -1));
for (const int d : drange) {
const int width = 1 << d;
submint e = 1;
for (int i = 0, j = 1; i < N; i += width * 2, j++) {
for (int l = i, r = i + width; l < i + width; l++, r++) {
if (rev) {
const submint x = as[l], y = as[r];
as[l] = x + y, as[r] = (x - y) * e;
} else {
const submint x = as[l], y = as[r] * e;
as[l] = x + y, as[r] = x - y;
}
}
e *= (rev ? irs : rs)[lsbp1(j) + 1];
}
}
if (rev) {
const submint iN = submint{N}.inv();
for (auto& a : as) {
a *= iN;
}
}
}
template<typename submint>
static Vec<submint> conv(const Vec<mint>& as, const Vec<mint>& bs, int sz)
{
const int an = std::min((int)as.size(), sz);
const int bn = std::min((int)bs.size(), sz);
const int M = an + bn - 1;
const int lg = clog(M);
const int L = 1 << lg;
Vec<submint> As(L), Bs(L);
for (int i : rep(an)) {
As[i] = as[i].val();
}
for (int i : rep(bn)) {
Bs[i] = bs[i].val();
}
trans(As, lg, false), trans(Bs, lg, false);
for (int i : rep(L)) {
As[i] *= Bs[i];
}
trans(As, lg, true);
const int N = std::min(sz, (int)as.size() + (int)bs.size() - 1);
As.resize(N);
return As;
}
static constexpr submint2 ip1 = submint2{submint1::mod()}.inv();
static constexpr submint3 ip2 = submint3{submint2::mod()}.inv();
static constexpr submint3 ip1p2 = submint3{submint1::mod()}.inv() * ip2;
static constexpr mint p1()
{
return mint{submint1::mod()};
}
static constexpr mint p1p2()
{
return p1() * mint{submint2::mod()};
}
static constexpr mint restore(int x1, int x2, int x3)
{
const int k0 = x1;
const int k1 = (ip1 * (x2 - k0)).val();
const int k2 = (ip1p2 * (x3 - k0) - ip2 * k1).val();
return p1p2() * k2 + p1() * k1 + k0;
}
};
template<typename mint, typename I>
mint divNth(FPS<mint> f, FPS<mint> g, I N)
{
if (f.size() == 0) { return 0; }
const int n = g.size();
int mi = 0;
mint a;
for (int i : rep(n)) {
if (g[i].val() != 0) {
mi = i;
a = g[i];
break;
}
}
g >>= mi;
const mint ia = a.inv();
for (auto& c : f) {
c *= ia;
}
for (auto& c : g) {
c *= ia;
}
FPS p = f.quot(g);
f -= g * p;
N += mi;
if (N < 0) { return 0; }
const mint offset = p.at(N);
for (; N > 0; N >>= 1) {
FPS mg = g;
for (int i = 1; i < n; i += 2) {
mg[i] = -mg[i];
}
const auto fmg = f * mg;
const auto gmg = g * mg;
f.clear(), g.clear();
for (int i = 0; i < gmg.size(); i += 2) {
g[i >> 1] = gmg[i];
}
if (N % 2 == 0) {
for (int i = 0; i < fmg.size(); i += 2) {
f[i >> 1] = fmg[i];
}
} else {
for (int i = 1; i < fmg.size(); i += 2) {
f[i >> 1] = fmg[i];
}
}
}
return offset + f.at(0);
}
template<typename mint, typename I>
mint nthTerm(const Vec<mint>& as, I N)
{
const FPS g{berlekampMassey(as)};
const int L = g.size();
const auto f = FPS<mint>{as}.mult(g, L - 1);
return divNth(f, g, N);
}
#pragma endregion
int main()
{
using mint = modint_1000000007;
const auto N = in.val<i64>() - 1;
const auto [A, B, K] = in.tup<mint, mint, mint>();
Vec<mint> As{A, B};
for (int i : rep(100)) {
const auto a = As[As.size() - 2], b = As[As.size() - 1];
const auto c = (b * b + K) / a;
As.push_back(c);
}
const auto ans = nthTerm(As, N);
out.ln(ans);
return 0;
}