結果
| 問題 | No.754 畳み込みの和 |
| コンテスト | |
| ユーザー |
 soraie_
|
| 提出日時 | 2021-03-20 10:26:30 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 949 ms / 5,000 ms |
| コード長 | 14,487 bytes |
| 記録 | |
| コンパイル時間 | 4,172 ms |
| コンパイル使用メモリ | 266,660 KB |
| 最終ジャッジ日時 | 2025-01-19 20:09:12 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 3 |
ソースコード
#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
//--------------------------------------------------------------------
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(n) for(ll _=0;_<(ll)n;++_)
#define rep2(i,n) for(ll i=0;i<(ll)n;++i)
#define rep3(i,a,b) for(ll i=(ll)a;i<(ll)b;++i)
#define rep4(i,a,b,c) for(ll i=(ll)a;i<(ll)b;i+=(ll)c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#ifdef _DEBUG
#define pass(...) __VA_ARGS__ ;
#define debug1(a) cerr<<#a<<": "<<a<<"\n"
#define debug2(a,b) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"
#define debug3(a,b,c) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"
#define debug4(a,b,c,d) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"
/*
#define debug1(a) cout<<#a<<": "<<a<<"\n"
#define debug2(a,b) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"
#define debug3(a,b,c) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"
#define debug4(a,b,c,d) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"
*/
#define debug(...) overload4(__VA_ARGS__,debug4,debug3,debug2,debug1)(__VA_ARGS__)
#define koko cerr << "koko\n";
#else
#define debug(...) void(0)
#define pass(...) void(0);
#define koko void(0);
#endif
#define mp make_pair
//#define fi first
//#define se second
void myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}
void doset(int n){cout << fixed << setprecision(n);cerr << fixed << setprecision(n);}
using ll = long long;
using ld = long double;
using dou = double;
template<class First,class Second>ostream& operator<<(ostream& os,const pair<First,Second>& pp)
{return os << "{" << pp.first << "," << pp.second << "}";}
template<class T>ostream& operator<<(ostream& os,const vector<T>& VV)
{if(VV.empty())return os<<"[]";os<<"[";rep(i,VV.size())os<<VV[i]<<(i==int(VV.size()-1)?"]":",");return os;}
template<class T>ostream& operator<<(ostream& os,const set<T>& SS)
{if(SS.empty())return os<<"[]";os<<"[";auto ii=SS.begin();for(;ii!=SS.end();ii++)os<<*ii<<(ii==prev(SS.end())?"]":",");return os;}
template<class Key,class Tp>ostream& operator<<(ostream& os,const map<Key,Tp>& MM)
{if(MM.empty())return os<<"[]";os<<"[";auto ii=MM.begin();for(;ii!=MM.end();ii++)os<<"{"<<ii->first<<":"<<ii->second<<"}"<<(ii==prev(MM.end())?"]":",");return os;}
const int inf = 1 << 30;
const ll INF = 1LL << 61;
const ld pi = 3.14159265358;
const ll mod1 = 1000000007LL;
const ll mod2 = 998244353LL;
typedef pair<ll,ll> P;
template<class T, class U> inline bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T, class U> inline bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; }
ll modpow(ll n,ll m,ll MOD){
if(m == 0)return 1;
if(m < 0)return 0;
ll res = 1;
n %= MOD;
while(m){
if(m & 1)res = (res * n) % MOD;
m >>= 1;
n *= n;
n %= MOD;
}
return res;
}
ll mypow(ll n,ll m){
if(m == 0)return 1;
if(m < 0)return -1;
ll res = 1;
while(m){
if(m & 1)res = (res * n);
m >>= 1;
n *= n;
}
return res;
}
inline bool isp(ll n){
bool res = true;
if(n == 1 || n == 0)return false;
else{
for(ll i = 2;i * i <= n;i++){
if(n % i == 0){
res = false;
break;
}
}
return res;
}
}
inline bool Yes(bool b = 1){cout << (b ? "Yes\n":"No\n");return b;}
inline bool YES(bool b = 1){cout << (b ? "YES\n":"NO\n");return b;}
map<ll,ll> primefactor(ll n){
map<ll,ll> ma;
if(n <= 1)return ma;
ll m = n;
for(ll i = 2;i * i <= n;i++){
while(m % i == 0){
ma[i]++;
m /= i;
}
}
if(m != 1)ma[m]++;
return ma;
}
vector<ll> divisor(ll n,bool sorted = true,bool samein = false){
vector<ll> res;
for(ll i = 1;i * i <= n;i++){
if(n % i == 0){
res.push_back(i);
if(i * i != n || samein)res.push_back(n / i);
}
}
if(sorted)sort(all(res));
return res;
}
ll __lcm(ll a,ll b){return a / __gcd(a,b) * b;}
template<class T>T sum(const vector<T> &V){T r=0;for(auto x:V)r+=x;return r;}
template<class T>T sum(const initializer_list<T> &V){T r=0;for(auto x:V)r+=x;return r;}
//#include <atcoder/all>
//#include "atcoder/lazysegtree.hpp"
//using namespace atcoder;
//--------------------------------------------------------------------
long long extgcd(long long a,long long b,long long &x,long long &y){
if(b == 0){
x = 1;
y = 0;
return a;
}
long long d = extgcd(b,a % b,y,x);
y -= a / b * x;
return d;
}
long long modinv(long long a,long long p){
long long b = p, u = 1, v = 0;
while(b){
long long t = a / b;
a -= t * b;std::swap(a, b);
u -= t * v;std::swap(u, v);
}
u %= p;
if(u < 0)u += p;
return u;
}
/**
* @brief garner precalc
* @return long long
*/
long long pregarner(std::vector<long long> &rems,std::vector<long long> &mods,long long MOD){
assert(rems.size() == mods.size());
for(int i = 0;i < int(rems.size());i++){
for(int j = 0;j < i;j++){
long long g = std::gcd(mods[i],mods[j]);
if((rems[i] - rems[j]) % g != 0)return -1;
mods[i] /= g;mods[j] /= g;
long long gi = std::gcd(g,mods[i]),gj = g / gi;
do{
g = std::gcd(gi,gj);
gi *= g;gj /= g;
}while(g != 1);
mods[i] *= gi;mods[j] *= gj;
rems[i] %= mods[i];rems[j] %= mods[j];
}
}
long long res = 1;
for(long long &a : mods)res = res * a % MOD;
return res;
}
/**
* @brief returns a integer where rems[i](mod.mods[i]).
* @return long long
*/
long long garner(std::vector<long long> rems,std::vector<long long> mods,long long MOD){
assert(rems.size() == mods.size());
mods.push_back(MOD);
int sz = mods.size();
std::vector<long long> cof(sz,1LL),con(sz,0LL);
for(int i = 0;i < sz - 1;i++){
long long cur = (rems[i] - con[i]) * modinv(cof[i],mods[i]) % mods[i];
if(cur < 0)cur += mods[i];
for(int j = i + 1;j < sz;j++){
con[j] = (con[j] + cur * cof[j]) % mods[j];
cof[j] = cof[j] * mods[i] % mods[j];
}
}
return con.back();
}
template<long long MOD = 1000000007>
struct modint {
using mint = modint<MOD>;
long long x;
modint(long long a = 0):x((a % MOD + MOD) % MOD){}
inline constexpr modint operator-()const noexcept{return modint(-x);}
inline constexpr modint &operator+=(const modint &a)noexcept{
if ((x += a.x) >= MOD) x -= MOD;
return *this;
}
inline constexpr modint &operator-=(const modint &a)noexcept{
if ((x -= a.x) < 0) x += MOD;
return *this;
}
inline constexpr modint &operator*=(const modint &a)noexcept{
(x *= a.x) %= MOD;
return *this;
}
inline constexpr modint &operator++()noexcept{
x++;
if(x == MOD)x = 0;
return *this;
}
inline constexpr modint operator++(int)noexcept{
modint res(*this);
operator++();
return res;
}
inline constexpr modint &operator--()noexcept{
x--;
if(x == -1)x = MOD - 1;
return *this;
}
inline constexpr modint operator--(int)noexcept{
modint res(*this);
operator--();
return res;
}
inline constexpr modint operator+(const modint &a)const noexcept{
modint res(*this);
return res += a;
}
inline constexpr modint operator-(const modint &a)const noexcept{
modint res(*this);
return res -= a;
}
inline constexpr modint operator*(const modint &a)const noexcept{
modint res(*this);
return res *= a;
}
inline constexpr modint inv()const{
long long a = x,b = MOD,u = 1,v = 0;
while(b){
long long t = a / b;
a -= t * b;std::swap(a,b);
u -= t * v;std::swap(u,v);
}
return u;
}
inline constexpr modint &operator/=(const modint &a)noexcept{return (*this) *= a.inv();}
inline constexpr modint operator/(const modint &a)const noexcept{
modint res(*this);
return res /= a;
}
inline constexpr bool operator==(const modint &a)const noexcept{return x == a.x;}
friend std::istream &operator>>(std::istream &is,modint &a) {
is >> a.x;
a.x = (a.x % MOD + MOD) % MOD;
return is;
}
friend std::ostream &operator<<(std::ostream &os,const modint &a){
os << a.x;
return os;
}
long long getmod(){return MOD;}
friend mint modpow(mint a,long long b)noexcept{
mint res(1);
while(b){
if(b & 1)res *= a;
a *= a;
b >>= 1;
}
return res;
}
};
//using mint = modint<1'000'000'007>::mint;
//ex. (2013265921,137,27),(998244353,31,23),(469762049,30,26)
template<long long MOD,int base,int max_exp>
struct NTT_primitive{
using mint = modint<MOD>;
std::vector<mint> bases,invs;
NTT_primitive(){
bases.resize(max_exp + 1);invs.resize(max_exp + 1);
bases[max_exp] = base;
invs[max_exp] = mint(base).inv();
for(int i = max_exp - 1;i >= 0;i--){
bases[i] = bases[i + 1] * bases[i + 1];
invs[i] = invs[i + 1] * invs[i + 1];
}
}
void dft(std::vector<mint>& vec,int t){
int sz = vec.size();
if(sz == 1)return;
std::vector<mint> veca,vecb;
for(int i = 0;i < sz / 2;i++){
veca.push_back(vec[i * 2]);
vecb.push_back(vec[i * 2 + 1]);
}
dft(veca,t);
dft(vecb,t);
int e = __builtin_ffsll(sz) - 1;
mint now = 1,zeta = (t == 1 ? bases[e]:invs[e]);
for(int i = 0;i < sz;i++){
vec[i] = veca[i % (sz / 2)] + now * vecb[i % (sz / 2)];
now *= zeta;
}
}
std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){
assert(A.size() == B.size());
int sz = 1;
while(sz < int(A.size() + B.size()))sz <<= 1;
std::vector<mint> f(sz),g(sz);
for(int i = 0;i < int(A.size());i++){
f[i] = A[i];
g[i] = B[i];
}
dft(f,1);dft(g,1);
for(int i = 0;i < sz;i++)f[i] = f[i] * g[i];
dft(f,-1);
mint inv = mint(sz).inv();
for(int i = 0;i < sz;i++)f[i] *= inv;
return f;
}
void dft(std::vector<long long>& vec,int t){
int sz = vec.size();
if(sz == 1)return;
std::vector<long long> veca,vecb;
for(int i = 0;i < sz / 2;i++){
veca.push_back(vec[i * 2]);
vecb.push_back(vec[i * 2 + 1]);
}
dft(veca,t);
dft(vecb,t);
int e = __builtin_ffsll(sz) - 1;
long long now = 1,zeta = (t == 1 ? bases[e].x:invs[e].x);
for(int i = 0;i < sz;i++){
vec[i] = (veca[i % (sz / 2)] + now * vecb[i % (sz / 2)] % MOD) % MOD;
now = now * zeta % MOD;
}
}
std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){
assert(A.size() == B.size());
int sz = 1;
while(sz < int(A.size() + B.size()))sz <<= 1;
std::vector<long long> f(sz),g(sz);
for(int i = 0;i < int(A.size());i++){
f[i] = A[i] % MOD;
g[i] = B[i] % MOD;
}
dft(f,1);dft(g,1);
for(int i = 0;i < sz;i++)f[i] = f[i] * g[i] % MOD;
dft(f,-1);
long long inv = modinv(sz,MOD);
for(int i = 0;i < sz;i++)f[i] = f[i] * inv % MOD;
return f;
}
};
template<long long MOD>
struct NTT_all{
NTT_primitive<2013265921,137,27> ntt1;
NTT_primitive<998244353,31,23> ntt2;
NTT_primitive<469762049,30,26> ntt3;
using mint = modint<MOD>;
using mint1 = modint<2013265921>;
using mint2 = modint<998244353>;
using mint3 = modint<469762049>;
NTT_all(){}
std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){
assert(A.size() == B.size());
int sz = A.size();
std::vector<mint1> A1(sz),B1(sz);
std::vector<mint2> A2(sz),B2(sz);
std::vector<mint3> A3(sz),B3(sz);
for(int i = 0;i < sz;i++){
A1[i] = A[i].x;A2[i] = A[i].x;A3[i] = A[i].x;
B1[i] = B[i].x;B2[i] = B[i].x;B3[i] = B[i].x;
}
auto C1 = ntt1.convolution(A1,B1);
auto C2 = ntt2.convolution(A2,B2);
auto C3 = ntt3.convolution(A3,B3);
int rs = C1.size();
std::vector<mint> res(rs);
for(int i = 0;i < rs;i++){
std::vector<long long> r = {C1[i].x,C2[i].x,C3[i].x},m = {2013265921,998244353,469762049};
res[i] = garner(r,m,MOD);
}
return res;
}
std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){
assert(A.size() == B.size());
int sz = A.size();
std::vector<long long> A1(sz),B1(sz),A2(sz),B2(sz),A3(sz),B3(sz);
for(int i = 0;i < sz;i++){
A1[i] = A[i] % 2013265921;B1[i] = B[i] % 2013265921;
A2[i] = A[i] % 998244353;B2[i] = B[i] % 998244353;
A3[i] = A[i] % 469762049;B3[i] = B[i] % 469762049;
}
auto C1 = ntt1.convolution(A1,B1);
auto C2 = ntt2.convolution(A2,B2);
auto C3 = ntt3.convolution(A3,B3);
int rs = C1.size();
std::vector<long long> res(rs);
for(int i = 0;i < rs;i++){
std::vector<long long> r = {C1[i],C2[i],C3[i]},m = {2013265921,998244353,469762049};
res[i] = garner(r,m,MOD) % MOD;
}
return res;
}
};
int main(){
myset();
NTT_all<mod1> ntt;
using mint = NTT_all<mod1>::mint;
int N;
cin >> N;
vector<mint> A(N + 1),B(N + 1);
rep(i,N + 1)cin >> A[i];
rep(i,N + 1)cin >> B[i];
// reverse(all(A));reverse(all(B));
auto C = ntt.convolution(A,B);
mint ans = 0;
rep(i,N + 1)ans += C[i];
cout << ans << "\n";
debug(A,B);
debug(C);
}