NTT模板

NTT(快速数论变换)用到的各种素数及原根：

https://blog.csdn.net/hnust_xx/article/details/76572828

NTT多项式乘法模板

#include<cstdio>
#include<iostream>
#include<algorithm>
 
using namespace std;
 
typedef long long LL;
 
const LL mod=; //119*2^23+1   g=3
 
const int N=(<<)+;
 
const int g=;
 
int rev[N];
 
LL a[N],b[N];
 
template<typename T>
void read(T &x)
{
    x=; char c=getchar();
    while(!isdigit(c)) c=getchar();
    while(isdigit(c)) { x=x*+c-''; c=getchar(); }
} 
 
LL Pow(LL a,LL b)
{
    LL res=;
    for(;b;a=a*a%mod,b>>=)
        if(b&) res=res*a%mod;
    return res;
}
 
void NTT(LL *a,int n,int f)
{
    for(int i=;i<n;++i)
        if(i<rev[i]) swap(a[i],a[rev[i]]);
    for(int i=;i<n;i<<=)
    {
        LL wn=Pow(g,(mod-)/(i*));
        if(f<) wn=Pow(wn,mod-);
        for(int j=,p=i<<;j<n;j+=p)
        {
            LL w=;
            for(int k=;k<i;++k,w=w*wn%mod)
            {
                int x=a[j+k],y=w*a[j+k+i]%mod;
                a[j+k]=(x+y)%mod; a[j+k+i]=(x-y+mod)%mod;
            }
        }
    }
    if(f<)
    {
        LL inv=Pow(n,mod-);
        for(int i=;i<n;++i) a[i]=a[i]*inv%mod;
    }
}
 
int main()
{
    int nn,mm;
    read(nn); read(mm);
    for(int i=;i<=nn;++i) read(a[i]);
    for(int i=;i<=mm;++i) read(b[i]);
    int l=,len=nn+mm;
    int n;
    for(n=;n<=len;n<<=) l++;
    for(int i=;i<n;++i) rev[i]=(rev[i>>]>>)|((i&)<<l-);
    NTT(a,n,);
    NTT(b,n,);
    for(int i=;i<n;++i) a[i]=a[i]*b[i]%mod;
    NTT(a,n,-);
    for(int i=;i<=len;++i) printf("%lld ",a[i]);
}