結果
| 問題 | No.215 素数サイコロと合成数サイコロ (3-Hard) |
| コンテスト | |
| ユーザー |
 zeta
|
| 提出日時 | 2026-03-06 05:04:10 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 790 ms / 4,000 ms |
| コード長 | 36,850 bytes |
| 記録 | |
| コンパイル時間 | 8,597 ms |
| コンパイル使用メモリ | 394,532 KB |
| 実行使用メモリ | 12,668 KB |
| 最終ジャッジ日時 | 2026-03-06 05:04:23 |
| 合計ジャッジ時間 | 8,554 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 2 |
コンパイルメッセージ
YRS/poly/coef_of_rationals.hpp: In instantiation of 'T fps_t<T>::coef_of_rationals_ntt(fps, fps, ll) [with T = mint_t<1000000007>; fps = std::vector<mint_t<1000000007>, std::allocator<mint_t<1000000007> > >; ll = long long int]': YRS/poly/coef_of_rationals.hpp:82:32: required from 'T fps_t<T>::coef_of_rationals(fps, fps, ll) [with T = mint_t<1000000007>; fps = std::vector<mint_t<1000000007>, std::allocator<mint_t<1000000007> > >; ll = long long int]' YRS/poly/coef_of_rationals.hpp:95:44: required from 'fps_t<T>::fps fps_t<T>::coef_of_rationals(fps, ll, ll) [with T = mint_t<1000000007>; fps = std::vector<mint_t<1000000007>, std::allocator<mint_t<1000000007> > >; ll = long long int]' No_215_素数サイコロと合成数サイコロ_3_Hard.cpp:33:33: required from here YRS/poly/coef_of_rationals.hpp:20:24: warning: left shift count is negative [-Wshift-count-negative]
ソースコード
#line 1 "No_215_\u7d20\u6570\u30b5\u30a4\u30b3\u30ed\u3068\u5408\u6210\u6570\u30b5\u30a4\u30b3\u30ed_3_Hard.cpp"
#define YRSD
#line 1 "YRS/aa/fast.hpp"
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#line 2 "YRS/all.hpp"
#line 2 "YRS/aa/head.hpp"
#include <iostream>
#include <algorithm>
#include <array>
#include <bitset>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <bit>
#include <chrono>
#include <functional>
#include <iomanip>
#include <utility>
#include <type_traits>
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <limits>
#include <ranges>
#include <concepts>
#define TE template <typename T>
#define TES template <typename T, typename ...S>
#define Z auto
#define ep emplace_back
#define eb emplace
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()
#define ov(a, b, c, d, e, ...) e
#define FO1(a) for (int _ = 0; _ < (a); ++_)
#define FO2(i, a) for (int i = 0; i < (a); ++i)
#define FO3(i, a, b) for (int i = (a); i < (b); ++i)
#define FO4(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(...) ov(__VA_ARGS__, FO4, FO3, FO2, FO1)(__VA_ARGS__)
#define FF1(a) for (int _ = (a) - 1; _ >= 0; --_)
#define FF2(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FF3(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define FF4(i, a, b, c) for (int i = (b) - 1; i >= (a); i -= (c))
#define FOR_R(...) ov(__VA_ARGS__, FF4, FF3, FF2, FF1)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t > -1; t = (t == 0 ? -1 : (t - 1) & s))
#define sort ranges::sort
using namespace std;
TE using vc = vector<T>;
TE using vvc = vc<vc<T>>;
TE using T1 = tuple<T>;
TE using T2 = tuple<T, T>;
TE using T3 = tuple<T, T, T>;
TE using T4 = tuple<T, T, T, T>;
TE using max_heap = priority_queue<T>;
TE using min_heap = priority_queue<T, vc<T>, greater<T>>;
using u8 = unsigned char; using uint = unsigned int; using ll = long long; using ull = unsigned long long;
using ld = long double; using i128 = __int128; using u128 = __uint128_t; using f128 = __float128;
using u16 = uint16_t;
using PII = pair<int, int>; using PLL = pair<ll, ll>;
#ifdef YRSD
constexpr bool dbg = 1;
#else
constexpr bool dbg = 0;
#endif
#line 2 "YRS/IO/IO.hpp"
istream &operator>>(istream &I, i128 &x) {
static string s;
I >> s;
int f = s[0] == '-';
x = 0;
const int N = (int)s.size();
FOR(i, f, N) x = x * 10 + s[i] - '0';
if (f) x = -x;
return I;
}
ostream &operator<<(ostream &O, i128 x) {
static string s;
s.clear();
bool f = x < 0;
if (f) x = -x;
while (x) s += '0' + x % 10, x /= 10;
if (s.empty()) s += '0';
if (f) s += '-';
reverse(all(s));
return O << s;
}
istream &operator>>(istream &I, f128 &x) {
static string s;
I >> s, x = stold(s);
return I;
}
ostream &operator<<(ostream &O, const f128 x) { return O << ld(x); }
template <typename... S>
istream &operator>>(istream &I, tuple<S...> &t) {
return apply([&I](Z &...s) { ((I >> s), ...); }, t), I;
}
template <typename T, typename U>
istream &operator>>(istream &I, pair<T, U> &x) {
return I >> x.fi >> x.se;
}
template <typename T, typename U>
ostream &operator<<(ostream &O, const pair<T, U> &x) {
return O << x.fi << ' ' << x.se;
}
TE requires requires(T &c) { begin(c); end(c); } and
(not is_same_v<decay_t<T>, string>)
istream &operator>>(istream &I, T &c) {
for (Z &e : c) I >> e;
return I;
}
TE requires requires(const T &c) { begin(c); end(c); } and
(not is_same_v<decay_t<T>, const char*>) and
(not is_same_v<decay_t<T>, string>) and
(not is_array_v<remove_reference_t<T>> or
not is_same_v<remove_extent_t<remove_reference_t<T>>, char>)
ostream &operator<<(ostream &O, const T &a) {
if (a.empty()) return O;
Z i = a.begin();
O << *i++;
for (; i != a.end(); ++i) O << ' ' << *i;
return O;
}
void IN() {}
TE void IN(T &x, Z &...s) { cin >> x, IN(s...); }
void print() { cout << '\n'; }
TES void print(T &&x, S &&...y) {
cout << x;
if constexpr (sizeof...(S)) cout << ' ';
print(forward<S>(y)...);
}
void put() {}
TES void put(T &&x, S &&...y) {
cout << x;
put(forward<S>(y)...);
}
#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define UINT(...) uint __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; IN(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__; IN(__VA_ARGS__)
#define I128(...) i128 __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; IN(__VA_ARGS__)
#define CH(...) char __VA_ARGS__; IN(__VA_ARGS__)
#define REAL(...) re __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(T, a, n) vc<T> a(n); IN(a)
void YES(bool o = 1) { print(o ? "YES" : "NO"); }
void Yes(bool o = 1) { print(o ? "Yes" : "No"); }
void yes(bool o = 1) { print(o ? "yes" : "no"); }
void NO(bool o = 1) { YES(not o); }
void No(bool o = 1) { Yes(not o); }
void no(bool o = 1) { yes(not o); }
void ALICE(bool o = 1) { print(o ? "ALICE" : "BOB"); }
void Alice(bool o = 1) { print(o ? "Alice" : "Bob"); }
void alice(bool o = 1) { print(o ? "alice" : "bob"); }
void BOB(bool o = 1) { ALICE(not o); }
void Bob(bool o = 1) { Alice(not o); }
void bob(bool o = 1) { alice(not o); }
void POSSIBLE(bool o = 1) { print(o ? "POSSIBLE" : "IMPOSSIBLE"); }
void Possible(bool o = 1) { print(o ? "Possible" : "Impossible"); }
void possible(bool o = 1) { print(o ? "possible" : "impossible"); }
void IMPOSSIBLE(bool o = 1) { POSSIBLE(not o); }
void Impossible(bool o = 1) { Possible(not o); }
void impossible(bool o = 1) { possible(not o); }
void TAK(bool o = 1) { print(o ? "TAK" : "NIE"); }
void NIE(bool o = 1) { TAK(not o); }
#line 5 "YRS/all.hpp"
#if (__cplusplus >= 202002L)
#include <numbers>
constexpr ld pi = numbers::pi_v<ld>;
#endif
TE constexpr T inf = numeric_limits<T>::max();
template <> constexpr i128 inf<i128> = i128(inf<ll>) * 2'000'000'000'000'000'000;
template <typename T, typename U>
constexpr pair<T, U> inf<pair<T, U>> = {inf<T>, inf<U>};
TE constexpr static inline int pc(T x) { return popcount(make_unsigned_t<T>(x)); }
constexpr static inline ll len(const Z &a) { return a.size(); }
void reverse(Z &a) { reverse(all(a)); }
void unique(Z &a) {
sort(a);
a.erase(unique(all(a)), a.end());
}
TE vc<int> inverse(const vc<T> &a) {
int N = len(a);
vc<int> b(N, -1);
FOR(i, N) if (a[i] != -1) b[a[i]] = i;
return b;
}
Z QMAX(const Z &a) { return *max_element(all(a)); }
Z QMIN(const Z &a) { return *min_element(all(a)); }
TE Z QMAX(T l, T r) { return *max_element(l, r); }
TE Z QMIN(T l, T r) { return *min_element(l, r); }
constexpr bool chmax(Z &a, const Z &b) { return (a < b ? a = b, 1 : 0); }
constexpr bool chmin(Z &a, const Z &b) { return (a > b ? a = b, 1 : 0); }
vc<int> argsort(const Z &a) {
vc<int> I(len(a));
iota(all(I), 0);
sort(I, [&](int i, int k) { return a[i] < a[k] or (a[i] == a[k] and i < k); });
return I;
}
TE vc<T> rearrange(const vc<T> &a, const vc<int> &I) {
int N = len(I);
vc<T> b(N);
FOR(i, N) b[i] = a[I[i]];
return b;
}
template <int of = 1, typename T>
vc<T> pre_sum(const vc<T> &a) {
int N = len(a);
vc<T> c(N + 1);
FOR(i, N) c[i + 1] = c[i] + a[i];
if (of == 0) c.erase(c.begin());
return c;
}
TE constexpr static int topbit(T x) {
if (x == 0) return - 1;
if constexpr (sizeof(T) <= 4) return 31 - __builtin_clz(x);
else return 63 - __builtin_clzll(x);
}
TE constexpr static int lowbit(T x) {
if (x == 0) return -1;
if constexpr (sizeof(T) <= 4) return __builtin_ctz(x);
else return __builtin_ctzll(x);
}
TE constexpr T floor(T x, T y) { return x / y - (x % y and (x ^ y) < 0); }
TE constexpr T ceil(T x, T y) { return floor(x + y - 1, y); }
TE constexpr T bmod(T x, T y) { return x - floor(x, y) * y; }
TE constexpr pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return pair{q, x - q * y};
}
template <typename T = ll>
T SUM(const Z &v) {
return accumulate(all(v), T(0));
}
int lb(const Z &a, Z x) { return lower_bound(all(a), x) - a.begin(); }
TE int lb(T l, T r, Z x) { return lower_bound(l, r, x) - l; }
int ub(const Z &a, Z x) { return upper_bound(all(a), x) - a.begin(); }
TE int ub(T l, T r, Z x) { return upper_bound(l, r, x) - l; }
template <bool ck = 1>
ll bina(Z f, ll l, ll r) {
if constexpr (ck) assert(f(l));
while (abs(l - r) > 1) {
ll x = (r + l) >> 1;
(f(x) ? l : r) = x;
}
return l;
}
TE T bina_real(Z f, T l, T r, int c = 100) {
while (c--) {
T x = (l + r) / 2;
(f(x) ? l : r) = x;
}
return (l + r) / 2;
}
Z pop(Z &s) {
if constexpr (requires { s.pop_back(); }) {
Z x = s.back();
return s.pop_back(), x;
} else if constexpr (requires { s.top(); }) {
Z x = s.top();
return s.pop(), x;
} else {
Z x = s.front();
return s.pop(), x;
}
}
void setp(int x) { cout << fixed << setprecision(x); }
TE inline void sh(vc<T> &a, int N, T b = {}) {
a.resize(N, b);
}
#line 2 "YRS/ds/basic/retsu.hpp"
TE struct retsu {
int N, M;
vc<T> a;
retsu(int N, int M, T bs = T()) : N(N), M(M), a(N * M, bs) {}
T* operator[](int i) { return a.data() + i * M; }
const T* operator[](int i) const { return a.data() + i * M; }
void fill(T x) { std::fill(all(a), x); }
T max() const { return QMAX(a); }
T min() const { return QMIN(a); }
inline int id(int x, int y) const { return x * M + y; }
void pres() {
FOR(i, 1, N) FOR(k, M) a[id(i, k)] += a[id(i - 1, k)];
FOR(i, N) FOR(k, 1, M) a[id(i, k)] += a[id(i, k - 1)];
}
inline T prod(int x, int y) const { return a[id(x, y)]; }
inline T prod(int l, int r, int a, int b) const {
return prod(r, b) + prod(l, a) - prod(l, b) - prod(r, a);
}
void reverse() {
FOR(i, N) FOR(k, M >> 1) swap(a[i * M + k], a[i * M + M - k - 1]);
}
vc<vc<T>> to_v() const {
vector c(N, vc<T>(M));
FOR(i, N) FOR(k, M) c[i][k] = a[id(i, k)];
return c;
}
};
TE istream &operator>>(istream &I, retsu<T> &a) {
for (Z &e : a.a) I >> e;
return I;
}
TE ostream &operator<<(ostream &O, retsu<T> &a) {
FOR(i, a.N) FOR(k, a.M) O << a[i][k] << " \n"[k + 1 == a.M and i + 1 != a.N];
return O;
}
#ifdef FIO
TE inline void rd(retsu<T> &a) {
for (T &x : a.a) rd(x);
}
TE inline void wt(retsu<T> &a) {
FOR(i, a.N) {
FOR(k, a.M) {
if (k) wt(' ');
wt(a[i][k]);
}
if (i != a.M) wt('\n');
}
}
#endif
#line 2 "YRS/poly/coef_of_rationals.hpp"
#line 2 "YRS/poly/poly_divmod.hpp"
#line 2 "YRS/poly/fps_div.hpp"
#line 2 "YRS/poly/c/bs.hpp"
#line 2 "YRS/poly/c/fps_t.hpp"
#line 2 "YRS/mod/mint_t.hpp"
#define c constexpr
template <int mod>
struct mint_t {
using T = mint_t;
static c uint m = mod;
uint x;
c inline uint val() const { return x; }
c mint_t() : x(0) {}
c mint_t(uint x) : x(x % m) {}
c mint_t(ull x) : x(x % m) {}
c mint_t(u128 x) : x(x % m) {}
c mint_t(int x) : x((x %= mod) < 0 ? x + mod : x) {}
c mint_t(ll x) : x((x %= mod) < 0 ? x + mod : x) {}
c mint_t(i128 x) : x((x %= mod) < 0 ? x + mod : x) {}
c T &operator+=(T p) {
if ((x += p.x) >= m) x -= m;
return *this;
}
c T &operator-=(T p) {
if ((x += m - p.x) >= m) x -= m;
return *this;
}
c T operator+(T p) const { return T(*this) += p; }
c T operator-(T p) const { return T(*this) -= p; }
c T &operator*=(T p) {
x = ull(x) * p.x % m;
return *this;
}
c T operator*(T p) const { return T(*this) *= p; }
c T &operator/=(T p) { return *this *= p.inv(); }
c T operator/(T p) const { return T(*this) /= p; }
c T operator-() const { return T::gen(x ? mod - x : 0); }
c T inv() const {
int a = x, b = mod, x = 1, y = 0;
while (b > 0) {
int t = a / b;
swap(a -= t * b, b);
swap(x -= t * y, y);
}
return T(x);
}
c T pow(ll k) const {
if (k < 0) return inv().pow(-k);
T s(1), a(x);
for (; k; k >>= 1, a *= a)
if (k & 1) s *= a;
return s;
}
c bool operator<(T p) const { return x < p.x; }
c bool operator==(T p) const { return x == p.x; }
c bool operator!=(T p) const { return x != p.x; }
static c T gen(uint x) {
T s;
s.x = x;
return s;
}
friend istream &operator>>(istream &cin, T &p) {
ll t;
cin >> t;
p = t;
return cin;
}
friend ostream &operator<<(ostream &cout, T p) { return cout << p.x; }
static c int get_mod() { return mod; }
static c PII ntt_info() {
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 998244353) return {23, 31};
if (mod == 120586241) return {20, 74066978};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 1004535809) return {21, 582313106};
if (mod == 1012924417) return {21, 368093570};
return {-1, -1};
}
static c bool can_ntt() { return ntt_info().fi != -1; }
};
#undef c
using M99 = mint_t<998244353>;
using M17 = mint_t<1000000007>;
using M11 = M17;
#ifdef FIO
template <int mod>
void rd(mint_t<mod> &x) {
LL(y);
x = y;
}
template <int mod>
void wt(mint_t<mod> x) {
wt(x.x);
}
#endif
#line 4 "YRS/poly/c/fps_t.hpp"
// 动态模数需要在 设置模数后 进行构造
TE struct fps_t {
using fps = vc<T>;
using cf = const fps &;
static inline const uint p = T::get_mod(), t = T::ntt_info().fi,
r = T::ntt_info().se;
static inline const ull M = ull(p) * p;
// 需要动态模数反复set mod的啥比题到底是谁在出
// static inline uint p = T::get_mod(), t = T::ntt_info().fi,
// r = T::ntt_info().se;
// static inline ull M = ull(p) * p;
// static void reset() {
// p = T::get_mod();
// tie(t, r) = T::ntt_info();
// M = ull(p) * p;
// }
fps fa{1, 1}, ifa{1, 1}, in{0, 1};
T inv(int);
T fac(int);
T ifac(int);
T C(int, int);
static constexpr int p0 = 167'772'161, p1 = 469'762'049, p2 = 754'974'721;
using f0 = fps_t<mint_t<p0>>;
using f1 = fps_t<mint_t<p1>>;
using f2 = fps_t<mint_t<p2>>;
static void sh(fps &, int);
static int count_terms(cf);
static T eval(cf, T);
T crt(ull, ull, ull);
u128 crt_128(ull, ull, ull);
static void ntr(T *, T *, T *, T *, T *, T *);
static void ntt(fps &, bool);
static void trans_ntt(fps &, bool);
static void ntt_db(fps &f, bool = 0);
fps conv_naive(cf, cf);
fps conv_kara(cf, cf);
static fps conv_ntt(fps, fps);
fps conv_mtt(cf, cf);
fps conv(cf, cf);
vc<int> conv_for_big(const vc<int> &, const vc<int> &);
static fps sq_ntt(fps);
fps sq_mtt(cf);
fps sq(cf);
fps diff(cf);
fps inte(cf);
T inte(cf, T, T);
fps mid_prod(cf, cf);
fps inv_sp(cf);
fps inv_ntt(cf);
fps inv_mtt(cf);
fps inv(cf);
fps div_sp(fps, fps);
fps div_ntt(cf, cf);
fps div_mtt(fps, fps);
fps div_dense(cf, cf);
fps div(cf, cf);
fps log_sp(cf);
fps log_dense(cf);
fps log(cf);
fps exp_sp(cf);
fps exp_ntt(cf);
fps exp_mtt(cf);
fps exp_dense(cf);
fps exp(cf);
fps pw_sp(cf, T);
fps pw_dense(cf, T);
fps pw(cf, T);
fps pow(cf, ll);
fps sqr_sp(cf);
fps sqr_ntt(cf);
fps sqr_dense(cf);
fps sqr(cf);
fps sqrt(cf);
fps conv_all(const vc<fps> &);
fps conv_all(fps);
fps eval_geo(fps, T, T, int);
fps inte_geo(fps, T, T);
struct subprod_t;
subprod_t subprod(cf);
fps eval_ntt(fps, fps);
fps eval(fps, fps);
fps inte(fps, fps);
fps shift(fps, T);
T lag(cf, T);
fps lag(cf, T, int);
T lag(cf, cf, T);
fps pow_proj_ntt(fps, fps, int);
fps pow_proj(fps, fps, int);
fps comp_slow(cf, cf);
fps comp_ntt(fps, fps);
fps comp_mtt(fps, fps);
fps comp(fps, fps);
fps comp_inv(fps);
pair<fps, fps> divmod(fps, cf);
fps modpow(cf, ll, cf);
fps prod_of_f_rk_x(fps, T, int);
fps prod_of_one_minus_xn(const vc<int> &, int);
fps prod_of_inv_one_minus_xn(const vc<int> &, int);
fps prod_of_one_plus_xn(const vc<int> &a, int);
fps prod_of_inv_one_plus_xn(const vc<int> &a, int);
pair<fps, fps> sum_of_rationals(vc<pair<fps, fps>>);
pair<fps, fps> sum_of_rationals_sp(cf, cf);
fps sum_of_exp_bx(cf, cf, int);
fps sum_of_pow(cf, int);
fps sum_of_pow(ll, ll, int);
fps sum_of_pow(cf, cf, int);
fps sum_of_binomail(fps, T, T);
fps subset_sum(const vc<int> &, int k);
fps subset_sum_lm(const vc<int> &, int k);
T coef_of_rationals_ntt(fps, fps, ll);
T coef_of_rationals_mtt(fps, fps, ll);
T coef_of_rationals(fps, fps, ll);
fps coef_of_rationals(fps, ll, ll);
fps find_line(cf);
T line_inte(cf a, ll N);
template <int>
struct fac_t;
template <int lg = 10>
fac_t<lg> fac_large();
fps p_to_ffp(cf);
fps ffp_to_p(cf);
fps ffp_conv_ntt(fps, fps);
fps ffp_conv_mtt(fps, fps);
fps ffp_conv(cf, cf);
fps sin(cf);
fps cos(cf);
fps asin(cf);
fps atan(cf);
fps comp_f_ex(cf);
fps comp_f_1_minus_ex(cf);
fps comp_f_ex_minus_1(cf);
fps comp_f_a_plus_bx(cf, T, T);
fps comp_f_aplusbx_div_cplusdx_fake(cf, T, T, T, T);
fps comp_f_aplusbx_div_cplusdx(cf, T, T, T, T);
fps comp_f_x_plus_1_divx(cf);
struct conv_t;
conv_t online_conv();
struct exp_t;
exp_t online_exp();
struct log_t;
log_t online_log();
struct inv_t;
inv_t online_inv();
struct div_t;
div_t online_div();
struct pow_t;
pow_t online_pow(T);
fps presum(cf, T);
fps sinh(int);
fps exp_x(int);
fps exp_invx(int);
fps E_S(int);
fps E(int);
fps E_n(int, int);
fps E_odd(int);
fps E_noempty(int);
fps C_R(int);
fps bell(int);
fps derange(int);
fps bernoulli(int);
fps partition(int);
fps count_label_dag(int);
fps count_label_dag_con(int);
fps count_label_undir(int);
fps count_label_undir_con(int);
fps count_label_unicycle(int);
fps count_label_bipartite(int, bool);
fps count_label_bcc_v(int);
T count_label_bcc_v_N(int);
fps count_label_bcc_e(int);
T count_label_bcc_e_N(int);
T count_label_tournament(int);
fps count_label_scc(int);
fps count_label_euler_undir(int);
fps count_label_tree(int);
fps count_unlabel_tree(int);
};
#line 4 "YRS/poly/c/bs.hpp"
TE Z fps_t<T>::inv(int n) -> T {
assert(0 <= n);
while (len(in) <= n) {
int k = len(in), q = (p + k - 1) / k, r = k * q - p;
in.ep(in[r] * T(q));
}
return in[n];
}
TE Z fps_t<T>::fac(int n) -> T {
if (n >= p) return 0;
while (len(fa) <= n) {
int k = len(fa);
fa.ep(fa[k - 1] * T(k));
}
return fa[n];
}
TE Z fps_t<T>::ifac(int n) -> T {
if (n < 0) return T(0);
while (len(ifa) <= n) ifa.ep(ifa.back() * inv(len(ifa)));
return ifa[n];
}
TE Z fps_t<T>::C(int n, int k) -> T {
assert(n >= 0);
if (k < 0 or n < k) return 0;
return fac(n) * ifac(k) * ifac(n - k);
}
TE Z fps_t<T>::sh(fps &a, int N) -> void { a.resize(N); }
// 非0项数量
TE Z fps_t<T>::count_terms(cf f) -> int {
int s = 0, N = len(f);
FOR(i, N) s += f[i].val() != 0;
return s;
}
TE Z fps_t<T>::eval(cf f, T x) -> T {
T s = 0, c = 1;
int N = len(f);
FOR(i, N) s += f[i] * c, c *= x;
return s;
}
TE Z fps_t<T>::crt(ull a, ull b, ull c) -> T {
constexpr ull x = 104'391'568, xx = 190'329'765;
ull t = (b - a + p1) * x % p1, s = a + t * p0;
t = (c - s % p2 + p2) * xx % p2;
return T(s) + T(t) * T(ull(p0) * p1);
}
TE Z fps_t<T>::ntr(T *w, T *iw, T *r, T *ir, T *b, T *ib) -> void {
w[t] = fps_t<T>::r, iw[t] = w[t].inv();
FOR_R(i, t) w[i] = w[i + 1] * w[i + 1], iw[i] = iw[i + 1] * iw[i + 1];
T s = 1, c = 1;
#define f(a, g) FOR(i, t - g + 1) a[i] = w[i + g] * s, s *= iw[i + g], i##a[i] = iw[i + g] * c, c *= w[i + g]
f(r, 2);
s = c = 1;
f(b, 3);
#undef f
}
TE Z fps_t<T>::ntt(fps &a, bool in) -> void {
assert(T::can_ntt());
const uint m = p;
static T w[30], iw[30], r[30], ir[30], b[30], ib[30];
static bool ok = 0;
if (ok == 0) ok = 1, ntr(w, iw, r, ir, b, ib);
#define f(k) a[i + of + k * p]
#define g(k) ull(f(k).val())
#define tp topbit(~s & -~s)
int N = len(a), n = topbit(N);
if (not in) {
int sz = 0;
while (sz < n) {
if (n - sz == 1) {
int p = 1 << (n - sz - 1);
T c = 1;
FOR(s, 1 << sz) {
int of = s << (n - sz);
FOR(i, p) {
T l = f(0), w = f(1) * c;
f(0) = l + w, f(1) = l - w;
}
c *= r[tp];
}
++sz;
} else {
int p = 1 << (n - sz - 2);
T c = 1, in = w[2];
FOR(s, 1 << sz) {
T rr = c * c, R = rr * c;
int of = s << (n - sz);
FOR(i, p) {
ull x = g(0), y = g(1) * c.val(), e = g(2) * rr.val(),
r = g(3) * R.val(), t = (y + M - r) % m * in.val();
f(0) = x + y + e + r;
f(1) = x + e + M + M - y - r;
f(2) = x + M - e + t;
f(3) = x + M + M - e - t;
}
c *= b[tp];
}
sz += 2;
}
}
} else {
T c = T(N).inv();
FOR(i, N) a[i] *= c;
int sz = n;
while (sz) {
if (sz == 1) {
int p = 1 << (n - sz);
T c = 1;
FOR(s, 1 << (sz - 1)) {
int of = s << (n - sz + 1);
FOR(i, p) {
ull l = g(0), r = g(1);
f(0) = l + r, f(1) = (m + l - r) * c.val();
}
c *= ir[tp];
}
--sz;
} else {
int p = 1 << (n - sz);
T c = 1, in = iw[2];
FOR(s, 1 << (sz - 2)) {
T rr = c * c, R = rr * c;
int of = s << (n - sz + 2);
FOR(i, p) {
ull x = g(0), y = g(1), e = g(2), r = g(3),
t = (m + e - r) * in.val() % m;
f(0) = x + y + e + r;
f(1) = (x + m - y + t) * c.val();
f(2) = (x + y + m + m - e - r) * rr.val();
f(3) = (x + m + m - y - t) * R.val();
}
c *= ib[tp];
}
sz -= 2;
}
}
}
}
#undef f
#undef g
#undef tp
TE Z fps_t<T>::conv_naive(cf a, cf b) -> fps {
int N = len(a), M = len(b), sz = N + M - 1;
if (not N or not M) return {};
if (N > M) return conv_naive(b, a);
fps c(sz);
FOR(i, N) FOR(k, M) c[i + k] += a[i] * b[k];
return c;
}
TE Z fps_t<T>::conv_kara(cf f, cf g) -> fps {
constexpr int lm = 30;
if (min(len(f), len(g)) <= lm) return conv_naive(f, g);
int N = max(len(f), len(g)), M = ceil(N, 2);
fps f1, f2, g1, g2;
if (len(f) < M) f1 = f;
if (len(f) >= M) f1 = {f.begin(), f.begin() + M};
if (len(f) >= M) f2 = {f.begin() + M, f.end()};
if (len(g) < M) g1 = g;
if (len(g) >= M) g1 = {g.begin(), g.begin() + M};
if (len(g) >= M) g2 = {g.begin() + M, g.end()};
fps a = conv_kara(f1, g1);
fps b = conv_kara(f2, g2);
FOR(i, len(f2)) f1[i] += f2[i];
FOR(i, len(g2)) g1[i] += g2[i];
fps c = conv_kara(f1, g1);
fps F(len(f) + len(g) - 1);
FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];
FOR(i, len(b)) F[2 * M + i] += b[i], c[i] -= b[i];
if (c.back() == T(0)) c.pop_back();
FOR(i, len(c)) if (c[i] != T(0)) F[M + i] += c[i];
return F;
}
TE Z fps_t<T>::conv_ntt(fps a, fps b) -> fps {
assert(T::can_ntt());
int N = len(a), M = len(b), sz = 1;
if (min(N, M) == 0) return {};
while (sz < N + M - 1) sz <<= 1;
sh(a, sz), sh(b, sz);
ntt(a, 0);
ntt(b, 0);
FOR(i, sz) a[i] *= b[i];
ntt(a, 1);
sh(a, N + M - 1);
return a;
}
TE Z fps_t<T>::conv_mtt(cf a, cf b) -> fps {
int N = len(a), M = len(b);
if (not N or not M) return {};
f0::fps a0(N), b0(M);
f1::fps a1(N), b1(M);
f2::fps a2(N), b2(M);
FOR(i, N) a0[i] = a[i].val(), a1[i] = a[i].val(), a2[i] = a[i].val();
FOR(i, M) b0[i] = b[i].val(), b1[i] = b[i].val(), b2[i] = b[i].val();
Z c0 = f0::conv_ntt(a0, b0);
Z c1 = f1::conv_ntt(a1, b1);
Z c2 = f2::conv_ntt(a2, b2);
fps c(len(c0));
FOR(i, N + M - 1) c[i] = crt(c0[i].val(), c1[i].val(), c2[i].val());
return c;
}
TE Z fps_t<T>::conv(cf a, cf b) -> fps {
int N = len(a), M = len(b);
if (min(N, M) == 0) return {};
if (T::can_ntt()) {
if (min(N, M) <= 50) return conv_kara(a, b);
return conv_ntt(a, b);
}
if (min(N, M) <= 200) return conv_kara(a, b);
return conv_mtt(a, b);
}
TE Z fps_t<T>::sq_ntt(fps a) -> fps {
assert(T::can_ntt());
int N = len(a), sz = 1;
if (N == 0) return {};
while (sz < N + N - 1) sz <<= 1;
sh(a, sz);
ntt(a, 0);
FOR(i, sz) a[i] *= a[i];
ntt(a, 1);
sh(a, N + N - 1);
return a;
}
TE Z fps_t<T>::sq_mtt(cf a) -> fps {
int N = len(a);
if (N == 0) return {};
f0::fps a0(N);
f1::fps a1(N);
f2::fps a2(N);
FOR(i, N) a0[i] = a[i].val(), a1[i] = a[i].val(), a2[i] = a[i].val();
Z c0 = f0::sq_ntt(a0);
Z c1 = f1::sq_ntt(a1);
Z c2 = f2::sq_ntt(a2);
fps c(len(c0));
FOR(i, N + N - 1) c[i] = crt(c0[i].val(), c1[i].val(), c2[i].val());
return c;
}
TE Z fps_t<T>::sq(cf a) -> fps {
int N = len(a);
if (T::can_ntt()) {
if (N <= 50) return conv_naive(a, a);
return sq_ntt(a);
}
if (N <= 150) return conv_kara(a, a);
return sq_mtt(a);
}
// 微分
TE Z fps_t<T>::diff(cf f) -> fps {
int N = len(f);
if (N <= 1) return {};
fps g(N - 1);
FOR(i, N - 1) g[i] = f[i + 1] * T(i + 1);
return g;
}
// 积分
TE Z fps_t<T>::inte(cf f) -> fps {
int N = len(f);
fps g(N + 1);
FOR(i, 1, N + 1) g[i] = f[i - 1] * inv(i);
return g;
}
// 定积分
TE Z fps_t<T>::inte(cf f, T l, T r) -> T {
T s = 0, L = 1, R = 1;
int N = len(f);
FOR(i, N) {
L *= l, R *= r;
s += inv(i + 1) * f[i] * (L - R);
}
return s;
}
#line 2 "YRS/poly/fps_inv.hpp"
#line 4 "YRS/poly/fps_inv.hpp"
TE Z fps_t<T>::inv_sp(cf f) -> fps {
int N = len(f);
vc<pair<int, T>> a;
FOR(i, 1, N) if (f[i] != T(0)) a.ep(i, f[i]);
fps g(N);
T t = T(1) / f[0];
g[0] = t;
FOR(i, 1, N) {
T s = 0;
for (Z &&[x, y] : a) {
if (x > i) break;
s -= y * g[i - x];
}
g[i] = s * t;
}
return g;
}
TE Z fps_t<T>::inv_ntt(cf a) -> fps {
fps s{T(1) / a[0]};
int N = len(a), n = 1;
s.reserve(N);
for (; n < N; n <<= 1) {
fps f(n << 1), g(n << 1);
int sz = min(N, n << 1);
FOR(i, sz) f[i] = a[i];
FOR(i, n) g[i] = s[i];
ntt(f, 0);
ntt(g, 0);
FOR(i, n << 1) f[i] *= g[i];
ntt(f, 1);
FOR(i, n) f[i] = 0;
ntt(f, 0);
FOR(i, n << 1) f[i] *= g[i];
ntt(f, 1);
FOR(i, n, sz) s.ep(-f[i]);
}
return s;
}
TE Z fps_t<T>::inv_mtt(cf a) -> fps {
int N = len(a), n = 1;
fps c{a[0].inv()}, p;
for (; n < N; n <<= 1) {
p = sq(c);
sh(p, n << 1);
fps f(begin(a), begin(a) + min(n << 1, N));
p = conv(p, f);
sh(c, n << 1);
FOR(i, n << 1) c[i] = c[i] + c[i] - p[i];
}
sh(c, N);
return c;
}
TE Z fps_t<T>::inv(cf f) -> fps {
int t = count_terms(f), c = T::can_ntt() ? 160 : 820;
if (t < c) return inv_sp(f);
return T::can_ntt() ? inv_ntt(f) : inv_mtt(f);
}
#line 5 "YRS/poly/fps_div.hpp"
TE Z fps_t<T>::div_sp(fps f, fps g) -> fps {
if (g[0].val() != 1) {
T c = g[0].inv();
for (T &x : f) x *= c;
for (T &x : g) x *= c;
}
vc<pair<int, T>> a;
int N = len(g);
FOR(i, 1, N) if (g[i].val() != 0) a.ep(i, -g[i]);
N = len(f);
FOR(i, N) for (Z &&[x, y] : a) if (i >= x) f[i] += y * f[i - x];
return f;
}
TE Z fps_t<T>::div_ntt(cf f, cf g) -> fps {
int N = len(f), M = len(g);
if (N == 1) return {f[0] / g[0]};
int m = 1;
while (m + m < N) m <<= 1;
fps a(m << 1), b(m << 1), c(g);
sh(c, m);
c = inv(c);
sh(c, m << 1);
ntt(c, 0);
FOR(i, m) a[i] = f[i];
FOR(i, m, N) a[i] = 0;
ntt(a, 0);
FOR(i, m << 1) a[i] *= c[i];
ntt(a, 1);
fps s(N);
FOR(i, m) s[i] = a[i];
FOR(i, m, m << 1) a[i] = 0;
ntt(a, 0);
FOR(i, min(m << 1, M)) b[i] = g[i];
FOR(i, min(m << 1, M), m << 1) b[i] = 0;
ntt(b, 0);
FOR(i, m << 1) a[i] *= b[i];
ntt(a, 1);
FOR(i, m) a[i] = 0;
FOR(i, m, min(m << 1, N)) a[i] -= f[i];
ntt(a, 0);
FOR(i, m << 1) a[i] *= c[i];
ntt(a, 1);
FOR(i, m, N) s[i] -= a[i];
return s;
}
TE Z fps_t<T>::div_mtt(fps f, fps g) -> fps {
int N = len(f);
sh(g, N);
g = inv(g);
f = conv(f, g);
sh(f, N);
return f;
}
TE Z fps_t<T>::div_dense(cf f, cf g) -> fps {
return T::can_ntt() ? div_ntt(f, g) : div_mtt(f, g);
}
TE Z fps_t<T>::div(cf f, cf g) -> fps {
if (count_terms(g) < 50) return div_sp(f, g);
return T::can_ntt() ? div_ntt(f, g) : div_mtt(f, g);
}
#line 4 "YRS/poly/poly_divmod.hpp"
// {q, r} of f/g
TE Z fps_t<T>::divmod(fps f, cf g) -> pair<fps, fps> {
assert(g.back() != 0);
int N = len(f), M = len(g);
if (N < M) return {{}, f};
fps a = f, b = g;
reverse(a);
reverse(b);
int d = N - M + 1;
sh(a, d);
sh(b, d);
a = div(a, b);
reverse(a);
b = conv(a, g);
FOR(i, N) f[i] -= b[i];
while (not f.empty() and f.back().val() == 0) pop(f);
return {a, f};
}
#line 2 "YRS/poly/c/ntt_db.hpp"
#line 2 "YRS/poly/c/trans_ntt.hpp"
#line 4 "YRS/poly/c/trans_ntt.hpp"
TE Z fps_t<T>::trans_ntt(vc<T> &a, bool in) -> void {
assert(T::can_ntt());
const uint m = T::get_mod();
static T w[30], iw[30], r[30], ir[30], b[30], ib[30];
static bool ok = 0;
if (ok == 0) ok = 1, ntr(w, iw, r, ir, b, ib);
#define f(k) a[i + of + k * p]
#define g(k) ull(f(k).val())
#define tp topbit(~s & -~s)
int N = len(a), n = topbit(N);
if (not in) {
int sz = n;
while (sz) {
if (sz == 1) {
int p = 1 << (n - sz);
T c = 1;
FOR(s, 1 << (sz - 1)) {
int of = s << (n - sz + 1);
FOR(i, p) {
T l = f(0), w = f(1) * c;
f(0) = l + w, f(1) = l - w;
}
c *= r[tp];
}
--sz;
} else {
int p = 1 << (n - sz);
T c = 1, in = w[2];
FOR(s, 1 << (sz - 2)) {
T rr = c * c, R = rr * c;
int of = s << (n - sz + 2);
FOR(i, p) {
ull x = g(0), y = g(1), e = g(2), r = g(3),
t = (m + e - r) * in.val() % m;
f(0) = x + y + e + r;
f(1) = (x + m - y + t) * c.val();
f(2) = (x + y + m + m - e - r) * rr.val();
f(3) = (x + m + m - y - t) * R.val();
}
c *= b[tp];
}
sz -= 2;
}
}
} else {
T c = T(N).inv();
FOR(i, N) a[i] *= c;
int sz = 0;
while (sz < n) {
T c = 1;
if (sz == n - 1) {
int p = 1 << (n - sz - 1);
FOR(s, 1 << sz) {
int of = s << (n - sz);
FOR(i, p) {
T l = f(0), w = f(1) * c;
f(0) = l + w, f(1) = l - w;
}
c *= ir[tp];
}
++sz;
} else {
int p = 1 << (n - sz - 2);
T in = iw[2];
FOR(s, 1 << sz) {
T rr = c * c, R = rr * c;
int of = s << (n - sz);
FOR(i, p) {
ull x = g(0), y = g(1) * c.val(), e = g(2) * rr.val(),
r = g(3) * R.val(), t = (y + M - r) % m * in.val();
f(0) = x + y + e + r;
f(1) = x + e + (2 * M - y - r);
f(2) = x + M - e + t;
f(3) = x + M + M - e - t;
}
c *= ib[tp];
}
sz += 2;
}
}
}
}
#undef f
#undef g
#undef tp
#line 5 "YRS/poly/c/ntt_db.hpp"
TE Z fps_t<T>::ntt_db(fps &a, bool tr) -> void {
static array<T, 30> rt;
static bool ok = 0;
if (not ok) {
ok = 1;
rt[t] = r;
FOR_R(i, t) rt[i] = rt[i + 1] * rt[i + 1];
}
if (not tr) {
int N = len(a);
Z b = a;
ntt(b, 1);
T s = 1, c = rt[topbit(N << 1)];
FOR(i, N) b[i] *= s, s *= c;
ntt(b, 0);
copy(all(b), back_inserter(a));
} else {
int N = len(a) >> 1;
fps t{a.begin(), a.begin() + N};
a = {a.begin() + N, a.end()};
trans_ntt(a, 0);
T s = 1, c = rt[topbit(N << 1)];
FOR(i, N) a[i] *= s, s *= c;
trans_ntt(a, 1);
FOR(i, N) a[i] += t[i];
}
}
#line 5 "YRS/poly/coef_of_rationals.hpp"
// single https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence
// range https://yukicoder.me/problems/no/215
TE Z fps_t<T>::coef_of_rationals_ntt(fps p, fps q, ll k) -> T {
assert(len(p) + 1 == len(q) and q[0] == T(1));
if (p.empty()) return 0;
int N = 1;
while (N < len(q)) N <<= 1;
fps w(N);
vc<int> b(N);
int n = topbit(N);
FOR(i, N) b[i] = (b[i >> 1] >> 1) + ((i & 1) << (n - 1));
const int t = T::ntt_info().fi;
const T r = T::ntt_info().se;
T s = r.inv().pow((1 << t) / (N << 1)), c = inv(2);
for (int i : b) w[i] = c, c *= s;
sh(p, N << 1);
sh(q, N << 1);
ntt(p, 0);
ntt(q, 0);
while (k >= N) {
if (not(k & 1)) {
FOR(i, N) {
p[i] = (p[i << 1] * q[i << 1 | 1] + p[i << 1 | 1] * q[i << 1]) * inv(2);
}
} else {
FOR(i, N) {
p[i] = (p[i << 1] * q[i << 1 | 1] - p[i << 1 | 1] * q[i << 1]) * w[i];
}
}
FOR(i, N) q[i] = q[i << 1] * q[i << 1 | 1];
sh(p, N);
sh(q, N);
k >>= 1;
if (k < N) break;
ntt_db(p), ntt_db(q);
}
ntt(p, 1), ntt(q, 1);
q = inv(q);
T res = 0;
FOR(i, k + 1) res += p[i] * q[k - i];
return res;
}
TE Z fps_t<T>::coef_of_rationals_mtt(fps p, fps q, ll k) -> T {
assert(len(p) + 1 == len(q) and q[0] == T(1));
if (p.empty()) return 0;
while (k >= len(p)) {
fps a(q);
int n = len(a);
FOR(i, n) if (i & 1) a[i] = -a[i];
p = conv(p, a);
q = conv(q, a);
FOR(i, n) q[i] = q[i << 1];
FOR(i, n - 1) p[i] = p[i << 1 | (k & 1)];
sh(p, n - 1);
sh(q, n);
k >>= 1;
}
return div(p, q)[k];
}
// [x^k]P/Q 求 ai=sum ci ai-j 则是 p / {1, -c1, -c2}
TE Z fps_t<T>::coef_of_rationals(fps p, fps q, ll k) -> T {
if (p.empty()) return {};
assert(len(q) > 0 and q[0] != T(0));
while (q.back().val() == 0) pop(q);
T c = q[0].inv(), s = 0;
for (T &x : p) x *= c;
for (T &x : q) x *= c;
if (len(p) >= len(q)) {
Z [f, g] = divmod(p, q);
s = (k < len(f) ? f[k] : T(0));
p = g;
}
sh(p, len(q) - 1);
if (T::can_ntt()) return s + coef_of_rationals_ntt(p, q, k);
return s + coef_of_rationals_mtt(p, q, k);
}
#line 2 "YRS/poly/mid_prod.hpp"
#line 4 "YRS/poly/mid_prod.hpp"
// n, m 次多項式 (n>=m) a, b → n-m 次多項式 c
// c[i] = sum_j b[j]a[i+j]
// a * ~b [M - 1, N - 1]
TE Z fps_t<T>::mid_prod(cf a, cf b) -> fps {
int N = len(a), M = len(b);
if (b.empty()) return fps(N + 1);
if (min(M, N - M + 1) <= 60) {
fps c(N - M + 1);
FOR(i, N - M + 1) FOR(k, M) c[i] += b[k] * a[i + k];
return c;
}
if (T::can_ntt()) {
int n = 1 << topbit(2 * N - 1);
fps fa(n), fb(n);
copy(all(a), fa.begin());
copy(b.rbegin(), b.rend(), fb.begin());
ntt(fa, 0);
ntt(fb, 0);
FOR(i, n) fa[i] *= fb[i];
ntt(fa, 1);
sh(fa, N);
fa.erase(fa.begin(), fa.begin() + M - 1);
return fa;
} else {
fps f(b.rbegin(), b.rend());
f = conv(a, f);
sh(f, N);
f.erase(f.begin(), f.begin() + M - 1);
return f;
}
}
#line 87 "YRS/poly/coef_of_rationals.hpp"
// N M 同阶 2e4 700ms, 1e5 5s | 1s N 7500 M 2e6, N 1e5 M 3e4
// coef [l, r) of 1 / q
TE Z fps_t<T>::coef_of_rationals(fps q, ll l, ll r) -> fps {
assert(not q.empty());
assert(q[0] == T(1));
assert(l <= r);
if (l == r) return {};
if (l + 1 == r) return {coef_of_rationals({T(1)}, q, l)};
ll m = r - l + 1;
if (len(q) > m) sh(q, m);
m = len(q);
fps f(q);
FOR(i, 1, m, 2) f[i] = -f[i];
q = conv(q, f);
int sz = len(q);
fps de((sz + 1) >> 1);
FOR(i, 0, sz, 2) de[i >> 1] = q[i];
ll s = 0, t = (r + 1) >> 1;
if (l + 2 > m) s = (l + 2 - m) >> 1;
fps x = coef_of_rationals(move(de), s, t), y(r - l + m - 1);
int a = len(x), b = len(y);
FOR(i, a) {
ll p = b - (r - 2 * (s + i));
if (0 <= p and p < b) y[p] = x[i];
}
reverse(f);
return mid_prod(y, f);
}
#line 6 "No_215_\u7d20\u6570\u30b5\u30a4\u30b3\u30ed\u3068\u5408\u6210\u6570\u30b5\u30a4\u30b3\u30ed_3_Hard.cpp"
using mint = M11;
using fps = vc<mint>;
fps_t<mint> X;
int sz;
fps gen(const vc<int> &a, int c) {
retsu<mint> dp(c + 1, sz);
dp[0][0] = 1;
for (int x : a) {
FOR_R(j, c) FOR_R(k, sz) if (dp[j][k].val() != 0) {
FOR(i, 1, c + 1) if (j + i <= c and k + i * x < sz) {
dp[j + i][k + i * x] += dp[j][k];
}
}
}
return {dp[c], dp[c] + sz};
}
void Yorisou() {
LL(N, P, C);
vc<int> a{2, 3, 5, 7, 11, 13}, b{4, 6, 8, 9, 10, 12};
sz = P * 13 + C * 12 + 1;
fps f = X.conv(gen(a, P), gen(b, C));
while (not f.empty() and f.back().val() == 0) pop(f);
fps cp = f, ls(sz << 1);
for (mint &x : f) x = -x;
f[0] += 1;
int d = min<ll>(N, sz);
fps coef = X.coef_of_rationals(f, N - d, N);
copy(all(coef), begin(ls) + sz - d);
ls = X.conv(ls, cp);
mint s;
FOR(i, sz, sz << 1) s += ls[i];
print(s);
}
constexpr int tests = 0, fl = 0, DB = 10;
#line 1 "YRS/aa/main.hpp"
int main() {
cin.tie(0)->sync_with_stdio(0);
int T = 1;
if (fl) cerr.tie(0);
if (tests and not fl) IN(T);
for (int i = 0; i < T or fl; ++i) {
Yorisou();
if (fl and i % DB == 0) cerr << "Case: " << i << '\n';
}
return 0;
}
#line 42 "No_215_\u7d20\u6570\u30b5\u30a4\u30b3\u30ed\u3068\u5408\u6210\u6570\u30b5\u30a4\u30b3\u30ed_3_Hard.cpp"