\[f_k=\sum_{i=1}^n {a_i}^k \]

\[\begin{aligned} F(x)&=\sum_{k \ge 0}x^k\sum_{i=1}^n {a_i}^k \\ &=\sum_{i=1}^n\sum_{k \ge 0}x^k {a_i}^k \\ &= \sum_{i=1}^n\frac{1}{1-a_ix} \\ &=\sum_{i=1}^n \left( 1 - \frac{-a_ix}{1-a_ix} \right) \\ &=n-\sum_{i=1}^n \frac{-a_ix}{1-a_ix} \\ &= n-x\sum_{i=1}^n \ln(1-a_ix)' \\ &= n-x \left( \ln \left( \prod_{i=1}^n 1-a_ix \right)\right)' \end{aligned}\]

分治 fft + 多项式 ln 即可，时间复杂度 \(\mathcal O(n \log^2 n)\)

#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
using namespace std;

const int MAXN = 8e6 , Mod = 998244353;
int Add( int x , int y ) { x += y; return x >= Mod ? x - Mod : x; }
int Sub( int x , int y ) { x -= y; return x < 0 ? x + Mod : x; }
int Mul( int x , int y ) { return 1ll * x * y % Mod; }
int Quick_pow( int x , int po ) { int Ans = 1; for( ; po ; po >>= 1 , x = Mul( x , x ) ) if( po & 1 ) Ans = Mul( Ans , x ); return Ans; }
int Inv( int x ) { return Quick_pow( x , Mod - 2 ); }
int iv[ MAXN + 5 ];
void Init() {
	iv[ 1 ] = 1;
	for( int i = 2 ; i <= MAXN ; i ++ ) iv[ i ] = Mul( Mod - Mod / i , iv[ Mod % i ] );
}

#define Poly vector< int >
#define len( x ) ( (int)x.size() )
Poly operator - ( int x , Poly f ) { for( int i = 0 ; i < len( f ) ; i ++ ) f[ i ] = Mod - f[ i ]; f[ 0 ] = Add( f[ 0 ] , x ); return f; }
Poly operator - ( Poly f , int x ) { f[ 0 ] = Sub( f[ 0 ] , x ); return f; }
Poly operator * ( Poly f , int x ) { for( int i = 0 ; i < len( f ) ; i ++ ) f[ i ] = Mul( f[ i ] , x ); return f; }
Poly operator + ( Poly f , Poly g ) {
	int n = max( len( f ) , len( g ) ); f.resize( n ); g.resize( n );
	for( int i = 0 ; i < n ; i ++ ) f[ i ] = Add( f[ i ] , g[ i ] );
	return f;
}
Poly operator - ( Poly f , Poly g ) {
	int n = max( len( f ) , len( g ) ); f.resize( n ); g.resize( n );
	for( int i = 0 ; i < n ; i ++ ) f[ i ] = Sub( f[ i ] , g[ i ] );
	return f;
}

const int G = 3 , IG = 332748118;
int lim , ilim , rev[ MAXN + 5 ];
void ntt( Poly &f , int op ) {
	for( int i = 0 ; i < lim ; i ++ ) if( i < rev[ i ] ) swap( f[ i ] , f[ rev[ i ] ] );
	for( int len = 2 , w ; len <= lim ; len <<= 1 ) {
		w = Quick_pow( op == 1 ? G : IG , ( Mod - 1 ) / len );
		for( int l = 0 ; l < lim ; l += len ) {
			for( int i = l , wk = 1 ; i < l + len / 2 ; i ++ , wk = Mul( wk , w ) ) {
				int t = Mul( wk , f[ i + len / 2 ] );
				f[ i + len / 2 ] = Sub( f[ i ] , t ); f[ i ] = Add( f[ i ] , t );
			}
		}
	}
	if( op == -1 ) for( int i = 0 ; i < lim ; i ++ ) f[ i ] = Mul( f[ i ] , ilim );
}
int mxlen = 100000000;
Poly operator * ( Poly f , Poly g ) {
	int n = len( f ) + len( g ) - 1; for( lim = 1 ; lim < n ; lim <<= 1 ); ilim = Inv( lim );
	for( int i = 0 ; i < lim ; i ++ ) rev[ i ] = ( rev[ i >> 1 ] >> 1 ) | ( i & 1 ? lim >> 1 : 0 );
	f.resize( lim ); g.resize( lim );
	ntt( f , 1 ); ntt( g , 1 );
	for( int i = 0 ; i < lim ; i ++ ) f[ i ] = Mul( f[ i ] , g[ i ] );
	ntt( f , -1 ); f.resize( min( n , mxlen ) );
	return f;
}
Poly Inv( Poly f ) {
	Poly g = Poly( 1 , Inv( f[ 0 ] ) );
	for( mxlen = 2 ; mxlen < 2 * len( f ) ; mxlen <<= 1 ) {
		Poly A = f; A.resize( mxlen );
		g = g * ( 2 - ( g * A ) ); 
	}
	g.resize( len( f ) ); return g;
}
Poly Der( Poly f ) {
	for( int i = 0 ; i < len( f ) - 1 ; i ++ ) f[ i ] = Mul( i + 1 , f[ i + 1 ] );
	f.resize( len( f ) - 1 );
	return f;
}
Poly Int( Poly f ) {
	f.resize( len( f ) + 1 );
	for( int i = len( f ) - 1 ; i >= 1 ; i -- ) f[ i ] = Mul( f[ i - 1 ] , iv[ i ] );
	f[ 0 ] = 0;
	return f;
}
Poly Ln( Poly f ) {
	Poly g = Int( Der( f ) * Inv( f ) );
	g.resize( len( f ) ); return g;
}
Poly Exp( Poly f ) {
	Poly g = Poly( 1 , 1 );
	for( mxlen = 2 ; mxlen < 4 * len( f ) ; mxlen <<= 1 ) {
		Poly A = f; A.resize( mxlen );
		g = g * ( ( 1 - Ln( g ) ) + A );
	}
	g.resize( len( f ) ); return g;
}
Poly Pow( Poly f , int k ) {
	f = Ln( f ); f = f * k; f = Exp( f );
	return f;
}
Poly Sqrt( Poly f ) {
	Poly g = Poly( 1 , 1 );
	for( mxlen = 2 ; mxlen < 4 * len( f ) ; mxlen <<= 1 ) {
		Poly A = f; A.resize( mxlen );
		g = ( g + ( A * Inv( g ) ) ) * Inv( 2 );
	}
	g.resize( len( f ) ); return g;
}

int T , n; Poly f[ MAXN + 5 ] , g;

Poly cdq_ntt( int l , int r ) {
	if( l == r ) return f[ l ];
	return cdq_ntt( l , ( l + r ) / 2 ) * cdq_ntt( ( l + r ) / 2 + 1 , r );
}

signed main( ) {
	Init();
	scanf("%d",&T);
	while( T -- ) {
		scanf("%d",&n);
		for( int i = 1 , a ; i <= n ; i ++ ) {
			scanf("%d",&a); f[ i ].resize( 2 );
			f[ i ][ 0 ] = 1 , f[ i ][ 1 ] = Mod - a;
		}
		g = Der( Ln( cdq_ntt( 1 , n ) ) );
		g.resize( len( g ) + 1 ); 
		for( int i = len( g ) - 1 ; i >= 1 ; i -- ) g[ i ] = g[ i - 1 ]; g[ 0 ] = 0;
		g = n - g;

		int Xor = 0;
		for( int i = 1 ; i <= n ; i ++ ) Xor ^= g[ i ];
		printf("%d\n", Xor );
	}
	return 0;
}