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test/convolution/NumberTheoreticalTransform-conv-fft.test.cpp
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- Last update: 2023-05-30 04:32:15+09:00
- Problem: https://yukicoder.me/problems/no/1307
Depends on
FastIO
(lib/00-util/FastIO.cpp)
- ModInt
(lib/00-util/ModInt.cpp)
- NumberTheoreticalTransform - 数論変換
(lib/31-convolution/NumberTheoreticalTransform.cpp)
Code
#define PROBLEM "https://yukicoder.me/problems/no/1307"
#include <vector>
#include <iostream>
#include <algorithm>
#include <array>
using namespace std;
#include "../../lib/00-util/ModInt.cpp"
#include "../../lib/00-util/FastIO.cpp"
#include "../../lib/31-convolution/NumberTheoreticalTransform.cpp"
constexpr long long MOD = 1000000000000000000LL;
int main() {
cin.tie(0);ios::sync_with_stdio(false);
int N,Q; read(N); read(Q);
vector<ModInt<MOD>> A(N),B(N,0),D(N,0);
for(int i=0;i<N;++i) {
int a; read(a);
A[i]=a;
}
while(Q--){
int r; read(r); B[N-1-r]+=1;
}
auto C = NumberTheoreticalTransform<MOD>::convolution(A,B);
for(int i=0;i<2*N-1;++i) {
D[(i+1)%N]+=C[i];
}
for(int i=0;i<N;++i) cout << D[i] << " \n"[i==N-1];
return 0;
}#line 1 "test/convolution/NumberTheoreticalTransform-conv-fft.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1307"
#include <vector>
#include <iostream>
#include <algorithm>
#include <array>
using namespace std;
#line 1 "lib/00-util/ModInt.cpp"
/*
* @title ModInt
* @docs md/util/ModInt.md
*/
template<long long mod> class ModInt {
public:
long long x;
constexpr ModInt():x(0) {}
constexpr ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {}
constexpr ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator+=(const long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator+=(const int y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator-=(const long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;}
constexpr ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;}
constexpr ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;}
constexpr ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;}
constexpr ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
constexpr ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
constexpr ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;}
constexpr ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;}
constexpr ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;}
constexpr ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;}
constexpr ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;}
constexpr ModInt operator-() const {return ModInt(-x); }
constexpr ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;}
constexpr ModInt operator--() {x--;if(x<0) x+=mod;return *this;}
constexpr ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
constexpr ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
constexpr ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
constexpr ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
constexpr ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }
constexpr bool operator==(const ModInt &p) const { return x == p.x; }
constexpr bool operator!=(const ModInt &p) const { return x != p.x; }
// ModInt inv() 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);}
constexpr ModInt inv() const {int a=x,b=mod,u=1,v=0,t=0,tmp=0;while(b > 0) {t = a / b;a-=t*b;tmp=a;a=b;b=tmp;u-=t*v;tmp=u;u=v;v=tmp;} return ModInt(u);}
constexpr ModInt pow(long long n) const {ModInt ret(1), mul(x);for(;n > 0;mul *= mul,n >>= 1) if(n & 1) ret *= mul;return ret;}
friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}
friend istream &operator>>(istream &is, ModInt &a) {long long t;is >> t;a = ModInt<mod>(t);return (is);}
};
constexpr long long MOD_998244353 = 998244353;
constexpr long long MOD_1000000007 = 1'000'000'000LL + 7; //'
#line 1 "lib/00-util/FastIO.cpp"
/*
* @title FastIO
* @docs md/util/FastIO.md
*/
class FastIO{
private:
inline static constexpr int ch_0='0';
inline static constexpr int ch_9='9';
inline static constexpr int ch_n='-';
inline static constexpr int ch_s=' ';
inline static constexpr int ch_l='\n';
inline static void endline_skip(char& ch) {
while(ch==ch_l) ch=getchar();
}
template<typename T> inline static void read_integer(T &x) {
int neg=0; char ch; x=0;
ch=getchar();
endline_skip(ch);
if(ch==ch_n) neg=1,ch=getchar();
for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0);
if(neg) x*=-1;
}
template<typename T> inline static void read_unsigned_integer(T &x) {
char ch; x=0;
ch=getchar();
endline_skip(ch);
for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0);
}
inline static void read_string(string &x) {
char ch; x="";
ch=getchar();
endline_skip(ch);
for(;(ch != ch_s && ch!=ch_l); ch = getchar()) x.push_back(ch);
}
inline static char ar[40];
inline static char *ch_ar;
template<typename T> inline static void write_integer(T x) {
ch_ar=ar;
if(x< 0) putchar(ch_n), x=-x;
if(x==0) putchar(ch_0);
for(;x;x/=10) *ch_ar++=(ch_0+x%10);
while(ch_ar--!=ar) putchar(*ch_ar);
}
public:
inline static void read(int &x) {read_integer<int>(x);}
inline static void read(long long &x) {read_integer<long long>(x);}
inline static void read(unsigned int &x) {read_unsigned_integer<unsigned int>(x);}
inline static void read(unsigned long long &x) {read_unsigned_integer<unsigned long long>(x);}
inline static void read(string &x) {read_string(x);}
inline static void read(__int128_t &x) {read_integer<__int128_t>(x);}
inline static void write(__int128_t x) {write_integer<__int128_t>(x);}
inline static void write(char x) {putchar(x);}
};
#define read(arg) FastIO::read(arg)
#define write(arg) FastIO::write(arg)
#line 1 "lib/31-convolution/NumberTheoreticalTransform.cpp"
/*
* @title NumberTheoreticalTransform - 数論変換
* @docs md/convolution/NumberTheoreticalTransform.md
*/
template<long long mod> class NumberTheoreticalTransform {
inline static constexpr int prime_1004535809 =1004535809;
inline static constexpr int prime_998244353 =998244353;
inline static constexpr int prime_985661441 =985661441;
inline static constexpr int prime_998244353_1004535809 = ModInt<prime_998244353>(prime_1004535809).inv().x;
inline static constexpr int prime_985661441_1004535809 = ModInt<prime_985661441>(prime_1004535809).inv().x;
inline static constexpr int prime_985661441_998244353 = ModInt<prime_985661441>(prime_998244353).inv().x;
inline static constexpr long long prime12=((long long)prime_1004535809) * prime_998244353;
inline static constexpr int log2n_max = 21;
template<int prime> inline static constexpr array<ModInt<prime>,log2n_max> get_pow2_inv() {
array<ModInt<prime>,log2n_max> ar;
ModInt<prime> v=1; ar[0]=v;
for(int i=1;i<log2n_max;++i) ar[i]=ar[i-1]/2;
return ar;
}
inline static constexpr array<ModInt<prime_1004535809>,log2n_max> pow2_inv_1004535809 = get_pow2_inv<prime_1004535809>();
inline static constexpr array<ModInt<prime_998244353>, log2n_max> pow2_inv_998244353 = get_pow2_inv<prime_998244353>();
inline static constexpr array<ModInt<prime_985661441>, log2n_max> pow2_inv_985661441 = get_pow2_inv<prime_985661441>();
template<int prime> inline static constexpr array<ModInt<prime>,log2n_max> get_base(int inv=0) {
array<ModInt<prime>,log2n_max> base, es, ies;
//TODO 3のハードコーディングを直す
ModInt<prime> e = ModInt<prime>(3).pow((prime - 1) >> log2n_max), ie = e.inv();
for (int i = log2n_max; i >= 2; --i) {
es[i - 2] = e, ies[i - 2] = ie;
e *= e, ie *= ie;
}
ModInt<prime> acc = 1;
if(!inv) {
for (int i = 0; i < log2n_max - 2; ++i) {
base[i] = es[i] * acc;
acc *= ies[i];
}
}
else {
for (int i = 0; i < log2n_max - 2; ++i) {
base[i] = ies[i] * acc;
acc *= es[i];
}
}
return base;
}
inline static constexpr array<ModInt<prime_1004535809>,log2n_max> base_1004535809=get_base<prime_1004535809>();
inline static constexpr array<ModInt<prime_1004535809>,log2n_max> ibase_1004535809=get_base<prime_1004535809>(1);
inline static constexpr array<ModInt<prime_998244353>,log2n_max> base_998244353=get_base<prime_998244353>();
inline static constexpr array<ModInt<prime_998244353>,log2n_max> ibase_998244353=get_base<prime_998244353>(1);
inline static constexpr array<ModInt<prime_985661441>,log2n_max> base_985661441=get_base<prime_985661441>();
inline static constexpr array<ModInt<prime_985661441>,log2n_max> ibase_985661441=get_base<prime_985661441>(1);
using Mint1 = ModInt<prime_1004535809>;
using Mint2 = ModInt<prime_998244353>;
using Mint3 = ModInt<prime_985661441>;
inline static ModInt<mod> garner(const Mint1& b1,const Mint2& b2,const Mint3& b3) {Mint2 t2 = (b2-b1.x)*prime_998244353_1004535809;Mint3 t3 = ((b3-b1.x)*prime_985661441_1004535809-t2.x)*prime_985661441_998244353;return ModInt<mod>(ModInt<mod>(prime12)*t3.x+b1.x+prime_1004535809*t2.x);}
template<long long prime> inline static void butterfly(vector<ModInt<prime>>& a, const array<ModInt<prime>,log2n_max>& base) {
int h = __builtin_ctz(a.size());
for (int i = 0; i < h; i++) {
int w = 1 << i, p = 1 << (h - (i+1));
ModInt<prime> acc = 1;
for (unsigned int s = 0; s < w; s++) {
int offset = s << (h - i);
for (int j = 0; j < p; ++j) {
auto l = a[j + offset];
auto r = a[j + offset + p] * acc;
a[j + offset] = l + r;
a[j + offset + p] = l - r;
}
acc *= base[__builtin_ctz(~s)];
}
}
}
template<long long prime> inline static void ibutterfly(vector<ModInt<prime>>& a, const array<ModInt<prime>,log2n_max>& base) {
int h = __builtin_ctz(a.size());
for (int i = h-1; 0 <= i; i--) {
int w = 1 << i, p = 1 << (h - (i+1));
ModInt<prime> acc = 1;
for (unsigned int s = 0; s < w; s++) {
int offset = s << (h - i);
for (int j = 0; j < p; ++j) {
auto l = a[j + offset];
auto r = a[j + offset + p];
a[j + offset] = l + r;
a[j + offset + p] = (l - r) * acc;
}
acc *= base[__builtin_ctz(~s)];
}
}
}
template<long long prime> inline static vector<ModInt<prime>> convolution_friendrymod(
const vector<ModInt<mod>>& a,
const vector<ModInt<mod>>& b,
const array<ModInt<prime>,log2n_max>& base,
const array<ModInt<prime>,log2n_max>& ibase,
const array<ModInt<prime>,log2n_max>& pow2_inv
){
int n = a.size(), m = b.size();
if (!n || !m) return {};
if (min(n, m) <= 60) {
vector<ModInt<prime>> f(n+m-1);
if (n >= m) for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) f[i+j]+=a[i].x*b[j].x;
else for (int j = 0; j < m; j++) for (int i = 0; i < n; i++) f[i+j]+=a[i].x*b[j].x;
return f;
}
int N,L,M=n+m-1; for(N=1,L=0;N<M;N*=2,++L);
ModInt<prime> inverse = pow2_inv[L];
vector<ModInt<prime>> g(N,0),h(N,0);
for(int i=0;i<a.size();++i) g[i]=a[i].x;
for(int i=0;i<b.size();++i) h[i]=b[i].x;
butterfly<prime>(g,base);
butterfly<prime>(h,base);
for(int i = 0; i < N; ++i) g[i] *= h[i];
ibutterfly<prime>(g,ibase);
for (int i = 0; i < n + m - 1; i++) g[i] *= inverse;
return g;
}
template<long long prime, long long ZZ> class Inner {
public:
inline static vector<ModInt<prime>> convolution_impl(const vector<ModInt<mod>>& g,const vector<ModInt<mod>>& h){
auto f1 = convolution_friendrymod<prime_1004535809>(g, h, base_1004535809, ibase_1004535809, pow2_inv_1004535809);
auto f2 = convolution_friendrymod<prime_998244353> (g, h, base_998244353, ibase_998244353, pow2_inv_998244353);
auto f3 = convolution_friendrymod<prime_985661441> (g, h, base_985661441, ibase_985661441, pow2_inv_985661441);
vector<ModInt<prime>> f(f1.size());
for(int i=0; i<f1.size(); ++i) f[i] = garner(f1[i],f2[i],f3[i]);
return f;
}
};
template<long long prime> class Inner<prime, prime_998244353> {
public:
inline static vector<ModInt<prime>> convolution_impl(const vector<ModInt<mod>>& g,const vector<ModInt<mod>>& h) {
return convolution_friendrymod<prime>(g,h,base_998244353,ibase_998244353,pow2_inv_998244353);
}
};
public:
inline static vector<ModInt<mod>> convolution(const vector<ModInt<mod>>& g,const vector<ModInt<mod>>& h){return Inner<mod,mod>::convolution_impl(g,h);}
};
#line 11 "test/convolution/NumberTheoreticalTransform-conv-fft.test.cpp"
constexpr long long MOD = 1000000000000000000LL;
int main() {
cin.tie(0);ios::sync_with_stdio(false);
int N,Q; read(N); read(Q);
vector<ModInt<MOD>> A(N),B(N,0),D(N,0);
for(int i=0;i<N;++i) {
int a; read(a);
A[i]=a;
}
while(Q--){
int r; read(r); B[N-1-r]+=1;
}
auto C = NumberTheoreticalTransform<MOD>::convolution(A,B);
for(int i=0;i<2*N-1;++i) {
D[(i+1)%N]+=C[i];
}
for(int i=0;i<N;++i) cout << D[i] << " \n"[i==N-1];
return 0;
}