【NTT】 HDOJ 5279 YJC plays Minecraft

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;

const int mod = 998244353;
const int maxn = 700005;

LL dp[100005],dp2[100005];
LL a[maxn], b[maxn], c[maxn], xp[maxn];
LL f[100005], g[100005];

LL powmod(LL a, LL b, LL p)
{
LL res = 1, base = a;
while(b) {
if(b % 2) res = res * base % mod;
base = base * base % mod;
b /= 2;
}
return res;
}

namespace NTT {
const int r = 3, gl = 25;
LL p, rp[50], irp[50];
void setMod(LL _p = 998244353) {
p = _p;
for(int i = 0; i < gl; i++) rp[i] = powmod(r, (p-1)/(1<<i), p);
}
void FFT(LL a[], int n, LL wt[] = rp)
{
for(int i = 0, j = 0; i < n; i++) {
if(j > i) swap(a[i], a[j]);
int k = n;
while(j & (k >>= 1)) j &= ~k;
j |= k;
}
for(int m = 1, b = 1; m < n; m<<=1, b++)
for(int k = 0, w = 1; k < m; ++k) {
for(int i = k; i < n; i += m<<1) {
int v = a[i+m] * w % p;
if((a[i+m] = a[i] - v) < 0) a[i+m] += p;
if((a[i] += v) >= p) a[i] -= p;
}
w = w * wt[b] % p;
}
}
void IFFT(LL a[], int n) {
for(int i = 0; i < gl; i++) irp[i] = powmod(rp[i], n-1, p);
FFT(a, n, irp);
LL inv = powmod(n, p-2, p);
for(int i = 0; i < n; i++) a[i] = a[i] * inv % p;
}
void Mul(LL a[], LL b[], LL n, LL c[]) {
FFT(a, n);FFT(b, n);
for(int i = 0; i < n; i++) c[i] = a[i] * b[i] % p;
IFFT(c, n);
}
}

LL f1(int x)
{
return dp[x] * g[x] % mod;
}

LL f2(int x)
{
return xp[x] * g[x-1] % mod;
}

void cdq(int L, int R)
{
if(L == R) {
if(L) dp[L] = dp[L] * f[L-1] % mod;
return;
}
int mid = (L + R) >> 1;
cdq(L, mid);
int N = R - L + 1, n = 1;
while(2 * N >= n) n *= 2;
for(int i = 0; i <= n; i++) a[i] = b[i] = c[i] = 0;
for(int i = 0; i < mid-L+1; i++) a[i] = f1(i + L);
for(int i = 1; i <= N; i++) b[i] = f2(i);
NTT::Mul(a, b, n, c);
for(int i = mid+1; i <= R; i++) dp[i] = (dp[i] + c[i-L]) % mod;
cdq(mid+1, R);
}

void init()
{
int N = 100000;
memset(dp, 0, sizeof dp);
memset(dp2, 0, sizeof dp2);

f[0] = 1;
for(int i = 1; i <= N; i++) f[i] = f[i-1] * i % mod;
g
= powmod(f
, mod-2, mod);
for(int i = N-1; i >= 0; i--) g[i] = g[i+1] * (i+1) % mod;
xp[1] = xp[2] = 1;
for(int i = 3; i <= N; i++) xp[i] = powmod(i, i-2, mod);

dp[0] = 1;
NTT::setMod();

cdq(0, N);

int n = 1;
while(2 * N >= n) n *= 2;

memset(a, 0, sizeof a);
memset(b, 0, sizeof b);
memset(c, 0, sizeof c);

for(int i = 0; i <= N; i++) a[i] = (dp[i] * g[i]) % mod;
for(int i = 2; i <= N; i++) b[i] = (xp[i] * g[i-2]) % mod;

NTT::Mul(a, b, n, c);

dp2[0] = dp2[1] = 1;
for(int i = 2; i <= N; i++) dp2[i] = (c[i] * f[i-2]) % mod;
}

void work()
{
int m, x;
scanf("%d", &m);
LL ans = 1, res = 1;
for(int i = 1; i <= m; i++) {
scanf("%d", &x);
ans = ans * dp[x] % mod;
res = res * dp2[x] % mod;
}
ans = ans * powmod(2, m, mod) % mod;
ans = ((ans - res) % mod + mod) % mod;
printf("%lld\n", ans);
}

int main()
{
init();

int _;
scanf("%d", &_);
while(_--) work();

return 0;
}