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| #include <bits/stdc++.h>
#define x first
#define y second
#define y1 Y1
#define y2 Y2
#define mp make_pair
#define pb push_back
#define DEBUG(x) cout << #x << " = " << x << endl;
using namespace std;
typedef long long LL;
typedef pair <int, int> pii;
template <typename T> inline int Chkmax (T &a, T b) { return a < b ? a = b, 1 : 0; }
template <typename T> inline int Chkmin (T &a, T b) { return a > b ? a = b, 1 : 0; }
template <typename T> inline T read ()
{
T sum = 0, fl = 1; char ch = getchar();
for (; !isdigit(ch); ch = getchar()) if (ch == '-') fl = -1;
for (; isdigit(ch); ch = getchar()) sum = (sum << 3) + (sum << 1) + ch - '0';
return sum * fl;
}
inline void proc_status ()
{
ifstream t ("/proc/self/status");
cerr << string (istreambuf_iterator <char> (t), istreambuf_iterator <char> ()) << endl;
}
const int Maxn = 21 + 5, Maxs = (1 << 21) + 5;
const int Mod = 998244353;
namespace MATH
{
inline void Add (int &a, int b) { if ((a += b) >= Mod) a -= Mod; }
inline int Pow (int a, int b)
{
int ans = 1;
for (int i = b; i; i >>= 1, a = (LL) a * a % Mod) if (i & 1) ans = (LL) ans * a % Mod;
return ans;
}
}
using namespace MATH;
int N, M, P, ALL;
int G[Maxn], W[Maxs], IW[Maxs];
int f[Maxn][Maxs], g[Maxn][Maxs];
namespace DSU
{
int fa[Maxn];
inline void init () { for (int i = 0; i < N; ++i) fa[i] = i; }
inline int get_fa (int x) { return fa[x] == x ? x : fa[x] = get_fa (fa[x]); }
inline void link (int x, int y) { fa[get_fa (x)] = get_fa (y); }
}
inline int check (int S)
{
static int deg[Maxn];
for (int i = 0; i < N; ++i) deg[i] = 0;
DSU :: init ();
for (int i = 0; i < N; ++i) if (S & (1 << i))
for (int j = i + 1; j < N; ++j) if ((S & (1 << j)) && (G[i] & (1 << j)))
DSU :: link (i, j), ++deg[i], ++deg[j];
int cnt = 0;
for (int i = 0; i < N; ++i) if ((1 << i) & S)
{
if (DSU :: fa[i] == i) ++cnt;
if (deg[i] & 1) return 1;
}
if (cnt > 1) return 1;
return 0;
}
inline void Init ()
{
ALL = (1 << N) - 1;
for (int i = 1; i <= ALL; ++i)
{
int p = i & (-i);
W[i] = (W[i ^ p] + W[p]) % Mod;
}
for (int i = 0; i <= ALL; ++i)
{
W[i] = Pow (W[i], P);
IW[i] = Pow (W[i], Mod - 2);
int len = __builtin_popcount (i);
if (check (i)) g[len][i] = W[i];
}
}
inline void DWT (int *A, int n, int fg)
{
for (int mid = 1; mid < n; mid <<= 1)
for (int i = 0, len = mid << 1; i < n; i += len)
for (int j = i; j < i + mid; ++j)
{
int x = A[j], y = A[j + mid];
if (!fg) A[j + mid] = (x + y) % Mod;
else A[j + mid] = (y - x + Mod) % Mod;
}
}
inline void Solve ()
{
Init ();
f[0][0] = 1;
DWT (f[0], 1 << N, 0);
for (int i = 0; i <= N; ++i) DWT (g[i], 1 << N, 0);
for (int i = 1; i <= N; ++i)
{
for (int j = 0; j < i; ++j)
for (int S = 0; S <= ALL; ++S)
Add (f[i][S], (LL) f[j][S] * g[i - j][S] % Mod);
DWT (f[i], 1 << N, 1);
for (int S = 0; S <= ALL; ++S) f[i][S] = (LL) f[i][S] * IW[S] % Mod;
DWT (f[i], 1 << N, 0);
}
DWT (f[N], 1 << N, 1);
printf("%d\n", f[N][ALL]);
}
inline void Input ()
{
N = read<int>(), M = read<int>(), P = read<int>();
for (int i = 1; i <= M; ++i)
{
int x = read<int>() - 1, y = read<int>() - 1;
G[x] |= (1 << y);
G[y] |= (1 << x);
}
for (int i = 0; i < N; ++i) W[1 << i] = read<int>();
}
int main()
{
#ifdef hk_cnyali
freopen("A.in", "r", stdin);
freopen("A.out", "w", stdout);
#endif
Input ();
Solve ();
return 0;
}
|
