Four issues of the polynomial - logarithmic polynomial

Problem: Given a number of $ n-1 $ polynomial $ F (x) $, find a polynomial $ G (x) $ such that $ G (x) \ equiv ln (F (x)) $ ($ mod $ $ x ^ {n} $)

(Guaranteed $ F (x) $ is the constant term 1)

This is relatively simple:

Sides derivative to give:

$G^{'}(x)\equiv \frac{F^{'}(x)}{F(x)}$($mod$ $x^{n}$)

On the right side it is known, the direct inverse polynomial can be calculated

Then both sides of the indefinite integral done, would have had a constant term, but considering the $ ln (F (0)) = ln1 = 0 = C $, and therefore the constant term can be directly 0

Code:

#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <queue>
#include <stack>
#define ll long long
using namespace std;
const ll mode=998244353;
ll f[100005];
ll g[100005];
int to[(1<<20)+5];
int n;
int lim=1,l=0;
ll pow_mul(ll x,ll y)
{
    ll ret=1;
    while(y)
    {
        if(y&1)ret=ret*x%mode;
        x=x*x%mode,y>>=1;
    }
    return ret;
}
void NTT(ll *a,int len,int k)
{
    ll inv=pow_mul(len,mode-2);
    for(int i=0;i<len;i++)if(i<to[i])swap(a[i],a[to[i]]);
    for(int i=1;i<len;i<<=1)
    {
        ll w0=pow_mul(3,(mode-1)/(i<<1));
        for(int j=0;j<len;j+=(i<<1))
        {
            ll w=1;
            for(int o=0;o<i;o++,w=w*w0%mode)
            {
                ll w1=a[j+o],w2=a[j+o+i]*w%mode;
                a[j+o]=(w1+w2)%mode,a[j+o+i]=((w1-w2)%mode+mode)%mode;
            }
        }
    }
    if(k==-1)
    {
        for(int i=1;i<(len>>1);i++)swap(a[i],a[len-i]);
        for(int i=0;i<len;i++)a[i]=a[i]*inv%mode;
    }
}
ll a[(1<<20)+5],b[(1<<20)+5],c[(1<<20)+5];
void get_inv(ll *f,ll *g,int dep)
{
    if(dep==1)
    {
        g[0]=pow_mul(f[0],mode-2);
        return;
    }
    int nxt=(dep+1)/2;
    get_inv(f,g,nxt);
    int lim=1,l=0;
    while(lim<=2*dep)lim<<=1,l++;
    for(int i=0;i<lim;i++)to[i]=((to[i>>1]>>1)|((i&1)<<(l-1)));
    for(int i=0;i<lim;i++)a[i]=b[i]=0;
    for(int i=0;i<dep;i++)a[i]=f[i];
    for(int i=0;i<nxt;i++)b[i]=g[i];
    NTT(a,lim,1),NTT(b,lim,1);
    for(int i=0;i<lim;i++)c[i]=a[i]*b[i]%mode*b[i]%mode;
    NTT(c,lim,-1);
    for(int i=0;i<dep;i++)g[i]=((2*g[i]-c[i])%mode+mode)%mode;
}
int main()
{
    scanf("%d",&n);
    for(int i=0;i<n;i++)scanf("%lld",&f[i]);
    get_inv(f,g,n);
    for(int i=0;i<n;i++)printf("%lld ",g[i]);
    printf("\n");
    return 0;
}