## Polynomial multiplicative inverse - NTT

Recursive solution to

``````#include <bits/stdc++.h>
using namespace std;
#define int long long
namespace NTT {
#define pw(n) (1<<n)
const int N=4000005; // 4 times!
const int mod=998244353,g=3;
int n,m,bit,bitnum,a[N+5],b[N+5],rev[N+5];
void getrev(int l){
for(int i=0;i<pw(l);i++){
rev[i]=(rev[i>>1]>>1)|((i&1)<<(l-1));
}
}
int fastpow(int a,int b){
int ans=1;
for(;b;b>>=1,a=1LL*a*a%mod){
if(b&1)ans=1LL*ans*a%mod;
}
return ans;
}
void NTT(int *s,int op){
for(int i=0;i<bit;i++)if(i<rev[i])swap(s[i],s[rev[i]]);
for(int i=1;i<bit;i<<=1){
int w=fastpow(g,(mod-1)/(i<<1));
for(int p=i<<1,j=0;j<bit;j+=p){
int wk=1;
for(int k=j;k<i+j;k++,wk=1LL*wk*w%mod){
int x=s[k],y=1LL*s[k+i]*wk%mod;
s[k]=(x+y)%mod;
s[k+i]=(x-y+mod)%mod;
}
}
}
if(op==-1){
reverse(s+1,s+bit);
int inv=fastpow(bit,mod-2);
for(int i=0;i<bit;i++)a[i]=1LL*a[i]*inv%mod;
}
}
void solve(vector <int> A,vector <int> B,vector <int> &C) {
n=A.size()-1;
m=B.size()-1;
for(int i=0;i<=n;i++) a[i]=A[i];
for(int i=0;i<=m;i++) b[i]=B[i];
m+=n;
bitnum=0;
for(bit=1;bit<=m;bit<<=1)bitnum++;
getrev(bitnum);
NTT(a,1);
NTT(b,1);
for(int i=0;i<bit;i++)a[i]=1LL*a[i]*b[i]%mod;
NTT(a,-1);
C.clear();
for(int i=0;i<=m;i++) C.push_back(a[i]);
for(int i=0;i<=min(m*2,N-1);i++) a[i]=b[i]=0;
}
}

const int N=4000005; // 4 times!
const int mod=998244353,g=3;

struct poly {
vector <int> a;
void cut(int n) {
while(a.size()>n) a.pop_back();
}
poly operator *(int b) {
poly c=*this;
for(int i=0;i<a.size();i++) (((c.a[i]*=b)%=mod)+=mod)%=mod;
return c;
}
poly operator *(const poly &b) {
poly c;
NTT::solve(a,b.a,c.a);
return c;
}
poly operator +(poly b) {
int len=max(a.size(),b.a.size());
a.resize(len);
b.a.resize(len);
poly c;
for(int i=0;i<len;i++) c.a.push_back((a[i]+b.a[i])%mod);
return c;
}
poly operator -(poly b) {
int len=max(a.size(),b.a.size());
a.resize(len);
b.a.resize(len);
poly c;
for(int i=0;i<len;i++) c.a.push_back(((a[i]-b.a[i])%mod+mod)%mod);
return c;
}
};

void print(poly x) {
for(int i=0;i<x.a.size();i++) cout<<x.a[i]<<" ";
cout<<endl;
}

int n,a[N];

int qpow(int p,int q) {
int r = 1;
for(; q; p*=p, p%=mod, q>>=1) if(q&1) r*=p, r%=mod;
return r;
}

int inv(int p) {
return qpow(p, mod-2);
}

poly solve(poly A, int n) {
A.cut(n);
poly B;
if(n==1) {
B.a.push_back(inv(A.a[0]));
}
else {

poly Bi = solve(A,(n-1)/2+1);
B = Bi*2 - A*Bi*Bi;
B.cut(n);
}
return B;
}

signed main() {
ios::sync_with_stdio(false);
cin>>n;
for(int i=0;i<n;i++) cin>>a[i];
poly A;
for(int i=0;i<n;i++) A.a.push_back(a[i]);
poly B = solve(A,n);
print(B);
}``````

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Origin www.cnblogs.com/mollnn/p/12316143.html
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