結果
| 問題 |
No.8046 yukicoderの過去問
|
| コンテスト | |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2020-01-24 17:07:41 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 141 ms / 2,000 ms |
| コード長 | 19,202 bytes |
| コンパイル時間 | 2,405 ms |
| コンパイル使用メモリ | 193,224 KB |
| 実行使用メモリ | 21,600 KB |
| 最終ジャッジ日時 | 2024-09-14 03:45:08 |
| 合計ジャッジ時間 | 3,628 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 9 |
ソースコード
#include <bits/stdc++.h>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define rep(i,N) for(long long i = 0; i < (long long)(N); i++)
#define repr(i,N) for(long long i = (long long)(N) - 1; i >= 0; i--)
#define rep1(i,N) for(long long i = 1; i <= (long long)(N) ; i++)
#define repr1(i,N) for(long long i = (N) ; (long long)(i) > 0 ; i--)
#define each(x,v) for(auto& x : v)
#define all(v) (v).begin(),(v).end()
#define sz(v) ((int)(v).size())
#define ini(...) int __VA_ARGS__; in(__VA_ARGS__)
#define inl(...) long long __VA_ARGS__; in(__VA_ARGS__)
#define ins(...) string __VA_ARGS__; in(__VA_ARGS__)
#define in2(N,s,t) rep(i,N){in(s[i] , t[i]);}
#define in3(N,s,t,u) rep(i,N){in(s[i] , t[i] , u[i]);}
using namespace std; void solve();
using ll = long long; template<class T = ll> using V = vector<T>;
using vi = V<int>; using vl = V<>; using vs = V<string>;
using vd = V<double>; using vvi = V< V<int> >; using vvl = V< V<> >;
template<typename T>using heap = priority_queue< T , V<T> , greater<T> >;
constexpr int inf = 1001001001; constexpr ll infLL = (1LL << 61) - 1;
struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya;
template<typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template<typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T, typename U> ostream& operator <<(ostream& os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; }
template<typename T, typename U> istream& operator >>(istream& is, pair<T, U> &p) { is >> p.first >> p.second; return is; }
template<typename T> ostream& operator <<(ostream& os, const vector<T> &v) { int s = (int)v.size(); rep(i,s) os << (i ? " " : "") << v[i]; return os; }
template<typename T> istream& operator >>(istream& is, vector<T> &v) { for(auto &x : v) is >> x; return is; }
void in(){} template <typename T,class... U> void in(T &t,U &...u){ cin >> t; in(u...);}
void out(){cout << "\n";} template <typename T,class... U> void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);}
template<typename T>void die(T x){out(x); exit(0);}
#ifdef NyaanDebug
#include "NyaanDebug.h"
#define trc(...) do { cerr << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0)
#define trca(v,N) do { cerr << #v << " = "; array_out(v , N);cout << endl;} while(0)
#else
#define trc(...)
#define trca(...)
int main(){solve();}
#endif
using P = pair<int,int>; using vp = V<P>;
constexpr int MOD = /**/ 1000000007; //*/ 998244353;
//////
template< int mod >
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int) (1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt< mod >(t);
return (is);
}
static int get_mod() { return mod; }
};
using modint = ModInt< MOD >;
namespace FastFourierTransform {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector< C > rts = { {0, 0},
{1, 0} };
vector< int > rev = {0, 1};
void ensure_base(int nbase) {
if(nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while(base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector< C > &a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
int need = (int) a.size() + (int) b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < sz; i++) {
int x = (i < (int) a.size() ? a[i] : 0);
int y = (i < (int) b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for(int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
fft(fa, sz >> 1);
vector< int64_t > ret(need);
for(int i = 0; i < need; i++) {
ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
};
template< typename T >
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
if(need == -1) need = a.size() + b.size() - 1;
int nbase = 0;
while((1 << nbase) < need) nbase++;
FastFourierTransform::ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < (int)a.size(); i++) {
fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
}
fft(fa, sz);
vector< C > fb(sz);
if(a == b) {
fb = fa;
} else {
for(int i = 0; i < (int)b.size(); i++) {
fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
}
fft(fb, sz);
}
real ratio = 0.25 / sz;
C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C a1 = (fa[i] + fa[j].conj());
C a2 = (fa[i] - fa[j].conj()) * r2;
C b1 = (fb[i] + fb[j].conj()) * r3;
C b2 = (fb[i] - fb[j].conj()) * r4;
if(i != j) {
C c1 = (fa[j] + fa[i].conj());
C c2 = (fa[j] - fa[i].conj()) * r2;
C d1 = (fb[j] + fb[i].conj()) * r3;
C d2 = (fb[j] - fb[i].conj()) * r4;
fa[i] = c1 * d1 + c2 * d2 * r5;
fb[i] = c1 * d2 + c2 * d1;
}
fa[j] = a1 * b1 + a2 * b2 * r5;
fb[j] = a1 * b2 + a2 * b1;
}
fft(fa, sz);
fft(fb, sz);
vector< T > ret(need);
for(int i = 0; i < need; i++) {
int64_t aa = llround(fa[i].x);
int64_t bb = llround(fb[i].x);
int64_t cc = llround(fa[i].y);
aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
ret[i] = aa + (bb << 15) + (cc << 30);
}
return ret;
}
};
template< int mod >
struct NumberTheoreticTransform {
int base, max_base, root;
vector< int > rev, rts;
NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while(mod_pow(root, (mod - 1) >> 1) == 1) ++root;
assert(mod_pow(root, mod - 1) == 1);
root = mod_pow(root, (mod - 1) >> max_base);
}
inline int mod_pow(int x, int n) {
int ret = 1;
while(n > 0) {
if(n & 1) ret = mul(ret, x);
x = mul(x, x);
n >>= 1;
}
return ret;
}
inline int inverse(int x) {
return mod_pow(x, mod - 2);
}
inline unsigned add(unsigned x, unsigned y) {
x += y;
if(x >= mod) x -= mod;
return x;
}
inline unsigned mul(unsigned a, unsigned b) {
return 1ull * a * b % (unsigned long long) mod;
}
void ensure_base(int nbase) {
if(nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
assert(nbase <= max_base);
while(base < nbase) {
int z = mod_pow(root, 1 << (max_base - 1 - base));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
rts[(i << 1) + 1] = mul(rts[i], z);
}
++base;
}
}
void ntt(vector< int > &a) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int j = 0; j < k; j++) {
int z = mul(a[i + j + k], rts[j + k]);
a[i + j + k] = add(a[i + j], mod - z);
a[i + j] = add(a[i + j], z);
}
}
}
}
vector< int > multiply(vector< int > a, vector< int > b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
int inv_sz = inverse(sz);
for(int i = 0; i < sz; i++) {
a[i] = mul(a[i], mul(b[i], inv_sz));
}
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
vector<modint> multiply_for_fps(const vector<modint> &a,const vector<modint> &b){
vector<int> A(a.size()) , B(b.size());
for(int i = 0;i < (int)a.size(); i++) A[i] = a[i].x;
for(int i = 0;i < (int)b.size(); i++) B[i] = b[i].x;
auto C = multiply( A , B );
vector<modint> ret(C.size());
for(int i = 0; i < (int)C.size() ;i++) ret[i].x = C[i];
return ret;
}
};
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
using MULT = function< P(P, P) >;
static MULT &get_mult() {
static MULT mult = nullptr;
return mult;
}
static void set_fft(MULT f) {
get_mult() = f;
}
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 T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
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];
shrink();
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
shrink();
return *this;
}
P &operator*=(const T &v) {
const int n = (int) this->size();
for(int k = 0; k < n; k++) (*this)[k] *= v;
return *this;
}
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
assert(get_mult() != nullptr);
return *this = get_mult()(*this, r);
}
P &operator%=(const P &r) {
return *this -= *this / r * r;
}
P operator-() const {
P ret(this->size());
for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return 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 pre(int sz) const {
return P(begin(*this), begin(*this) + min((int) this->size(), sz));
}
P operator>>(int sz) const {
if(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;
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
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;
}
// 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 ret({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == 1);
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
P sqrt(int deg = -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) << (i / 2);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
P ret({T(1)});
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);
}
// F(0) must be 0
P exp(int deg = -1) const {
assert((*this)[0] == T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1)});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
P pow(int64_t k, int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
for(int i = 0; i < n; i++) {
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P C(*this * rev);
P D(n - i);
for(int j = i; j < n; j++) D[j - i] = C[j];
D = (D.log() * k).exp() * (*this)[i].pow(k);
P E(deg);
if(i * k > deg) return E;
auto S = i * k;
for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j];
return E;
}
}
return *this;
}
T eval(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
};
using FPS = FormalPowerSeries< modint >;
// fにa * x^n + bを掛ける
void mul_simple(FPS &f,modint a ,int n, modint b){
for(int i = (int)f.size() - 1 ; i >= 0 ; i--){
f[i] *= b;
if(i >= n) f[i] += f[i - n] * a;
}
}
// fからa * x^n + bを割る
void div_simple(FPS &f,modint a,int n,modint b){
for(int i = 0 ; i < (int)f.size() ; i++){
f[i] /= b;
if(i + n < (int)f.size() ) f[n + i] -= f[i] * a;
}
}
// f / gをdeg(f)次まで求める
FPS div_(FPS &f , FPS g){
int n = f.size();
return (f * g.inv(n)).pre(n);
}
// solve関数内で
//
// FPS::set_fft(mul);
//
// とすること。
/**
NumberTheoreticTransform<MOD> ntt;
auto mul = [&](const FPS::P &a, const FPS::P &b) {
auto ret =ntt.multiply_for_fps(a , b);
return FPS::P(ret.begin(), ret.end());
};
/*///
//*/
// 下記のリンクを実装(kitamasa法のモンゴメリ乗算を使わない版)
// http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
// k項間漸化式のa_Nを求める O(k log k log N)
// N ... 求めたい項 (0-indexed)
// Q ... 漸化式 (1 - \sum_i c_i x^i)の形
// a ... 初期解 (a_0 , a_1 , ... , a_k-1)
// x^N を fでわった剰余を求め、aと内積を取る
modint kitamasa(ll N, FPS &Q, FPS &a){
int k = Q.size() - 1;
assert( (int)a.size() == k );
FPS P = a * Q; P.resize(k);
while(N){
auto Q2 = Q;
for(int i = 1; i < (int)Q2.size(); i += 2) Q2[i].x = MOD - Q2[i].x;
auto S = P * Q2;
auto T = Q * Q2;
if(N & 1){
for(int i = 1 ; i < (int)S.size() ; i += 2) P[i>>1].x = S[i].x;
for(int i = 0 ; i < (int)T.size() ; i += 2) Q[i>>1].x = T[i].x;
}
else{
for(int i = 0 ; i < (int)S.size() ; i += 2) P[i>>1].x = S[i].x;
for(int i = 0 ; i < (int)T.size() ; i += 2) Q[i>>1].x = T[i].x;
}
N >>= 1;
}
return P[0];
}
void solve(){
ArbitraryModConvolution< modint > fft;
auto mul = [&](const FPS::P &a, const FPS::P &b) {
auto ret = fft.multiply(a, b);
return FPS::P(ret.begin(), ret.end());
};
FPS::set_fft(mul);
ini(K , N);
FPS f(K + 1);
f[0] = 1;
rep(i , N){
ini(x);
f[x] = -1;
}
//trc(f);
f = f.inv(K + 1);
out(f[K]);
}