1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
| #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN = 100005, MAXM = 20005;
const ll MOD = 998244353, G = 3;
inline ll qpow(ll a, ll k) {
ll ret = 1;
while (k) {
if (k & 1) ret = ret * a % MOD;
a = a * a % MOD;
k >>= 1;
}
return ret;
}
namespace FFT {
int n, r[MAXN << 1];
void NTT(ll *a, int op) {
int k = 0;
for (; (1 << k) < n; ++k);
for (int i = 0; i < n; ++i) {
r[i] = r[i >> 1] >> 1 | (i & 1) << (k - 1);
if (i < r[i]) swap(a[i], a[r[i]]);
}
for (int l = 2; l <= n; l <<= 1) {
int m = l >> 1;
ll w = qpow(G, (MOD - 1) / l);
if (op == -1) w = qpow(w, MOD - 2);
for (int i = 0; i < n; i += l) {
ll wk = 1;
for (int j = 0; j < m; ++j, wk = wk * w % MOD) {
ll p = a[i + j], q = wk * a[i + j + m] % MOD;
a[i + j] = (p + q) % MOD;
a[i + j + m] = (p - q + MOD) % MOD;
}
}
}
}
void DFT(ll *a) {
NTT(a, 1);
}
void IDFT(ll *a) {
NTT(a, -1);
ll inv = qpow(n, MOD - 2);
for (int i = 0; i < n; ++i)
a[i] = a[i] * inv % MOD;
}
}
int m, n, k;
int a[MAXM];
vector<ll> b[MAXM << 1];
priority_queue<pair<int, int> > q;
ll x[MAXN << 1], y[MAXN << 1], ans;
ll fac[MAXN], inv[MAXN], facinv[MAXN];
inline ll C(int n, int k) {
return fac[n] * facinv[k] % MOD * facinv[n - k] % MOD;
}
int main() {
scanf("%d%d%d", &m, &n, &k);
fac[0] = facinv[0] = 1;
fac[1] = inv[1] = facinv[1] = 1;
for (int i = 2; i <= n; ++i) {
fac[i] = fac[i - 1] * i % MOD;
inv[i] = (MOD - MOD / i) * inv[MOD % i] % MOD;
facinv[i] = facinv[i - 1] * inv[i] % MOD;
}
for (int i = 1; i <= m; ++i) {
scanf("%d", &a[i]);
for (int j = 0; j < a[i]; ++j)
b[i].push_back(C(a[i], j) * fac[a[i] - 1] % MOD * facinv[a[i] - j - 1] % MOD);
q.push(make_pair(-b[i].size(), i));
}
int cnt = m;
while (q.size() > 1) {
int id1 = q.top().second, sz1 = -q.top().first;
q.pop();
int id2 = q.top().second, sz2 = -q.top().first;
q.pop();
FFT::n = 1;
while (FFT::n <= sz1 + sz2) FFT::n <<= 1;
for (int i = 0; i <= FFT::n; ++i) x[i] = y[i] = 0;
for (int i = 0; i < sz1; ++i) x[i] = b[id1][i];
for (int i = 0; i < sz2; ++i) y[i] = b[id2][i];
FFT::DFT(x), FFT::DFT(y);
for (int i = 0; i <= FFT::n; ++i) x[i] = x[i] * y[i] % MOD;
FFT::IDFT(x);
cnt++;
for (int i = 0; i <= sz1 + sz2 - 2; ++i)
b[cnt].push_back(x[i]);
q.push(make_pair(-b[cnt].size(), cnt));
}
int id = q.top().second, sz = -q.top().first;
for (int i = k; i < sz; ++i) {
ll tmp = C(i, k) * fac[n - i] % MOD * b[id][i] % MOD;
if ((i - k) & 1) ans = (ans - tmp + MOD) % MOD;
else ans = (ans + tmp) % MOD;
}
for (int i = 1; i <= m; ++i)
ans = ans * qpow(fac[a[i]], MOD - 2) % MOD;
printf("%lld", ans);
return 0;
}
|