#include <bits/stdc++.h>
#define ll long long
#define pii pair <int, int>
#define fi first
#define se second
#define pb push_back
#define pil pair <int, ll> 
#define LL __int128

using namespace std;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
const int N = 65, S = 10005; 
const ll mod = 11920928955078125, inf = 0x3f3f3f3f3f3f3f3f, imod = mod/5*4; 
int n, m, c, mk[N][N], vis[N], sm[N], sk[N]; 
ll M, w[N], v[N], k, dis[N][N], f[N][N][S], g[S]; 
vector <pil> e[N];

void dfs (int rt, int p, int fa) {
	for (auto i : e[p]) {
		if (i.fi == fa) continue; 
		dis[rt][i.fi] = dis[rt][p]+i.se; dfs(rt, i.fi, p); 
	}
}

struct val {
	ll v, c; 
	friend val operator * (const val & a, const val & b) {
		return (val){a.v+b.v, a.c*b.c}; 
	} 
	friend val operator + (const val & a, const val & b) {
		if (a.v^b.v) return a.v > b.v ? a : b; 
		return (val){a.v, a.c+b.c};  
	}
	void clr () {
		v = -inf; c = 0; 
	}
}fs[N][S], gs[S]; 

vector <int> td; 
void dp (int p, int fa) {
	if (mk[p][fa]) return; 
	mk[p][fa] = 1; 
	if (w[p] <= m) f[p][fa][w[p]] = v[p]; 
	for (auto i : e[p]) {
		if (i.fi == fa) continue; 
		dp(i.fi, p); 
		memset(g, -0x3f, sizeof g);
		td.clear(); 
		for (int j = 0;j <= m;j++) if (f[i.fi][p][j] >= 0) td.pb(j); 
		for (int j = 0;j <= m;j++) {
			if (f[p][fa][j] < 0) continue; 
			for (int z : td) if (j+z <= m) g[j+z] = max(g[j+z], f[i.fi][p][z]+f[p][fa][j]); 
		} 
		memcpy(f[p][fa], g, sizeof g); 
	}
	f[p][fa][0] = 0; 
}
inline bool chk (int i, int j) {
	return v[j] == 0 || dis[i][j] <= M/v[j]; 
}

void dp1 (int p, int fa) {
	for (int j = 0;j <= m;j++) fs[p][j].clr();
	if (vis[p]) {
		if (w[p] <= m) fs[p][w[p]] = (val){v[p], 1}; 
		for (auto i : e[p]) {
			if (i.fi == fa) continue; 
			dp1(i.fi, p);
			td.clear(); 
			for (int j = 0;j <= m;j++) gs[j].clr(); 
			for (int j = 0;j <= m;j++) if (fs[i.fi][j].v >= 0) td.pb(j); 
			for (int j = 0;j <= m;j++) {
				if (fs[p][j].v < 0) continue;
				for (int z : td) if (j+z <= m) {
					gs[j+z] = gs[j+z]+(fs[p][j]*fs[i.fi][z]);  
					
				}
			}
			memcpy(fs[p], gs, sizeof gs); 
		}
	}
	if (!sk[p]) fs[p][0] = (val){0, 1}; 
}

ll qpow (LL x, ll y = imod-1) {
	LL res = 1;
	while (y) {
		if (y&1) res = res*x%mod;
		x = x*x%mod; y >>= 1;
	}
	return res; 
}

ll lC (ll n, ll m) {
	if (m > n) return 0; 
	if (m > n-m) m = n-m; 
	LL res = 1; 
	ll c = 0, x = 1; 
	LL k = n; while (k) c += k/5, k /= 5; 
	k = m; while (k) c -= k/5, k /= 5; 
	k = n-m; while (k) c -= k/5, k /= 5;
	if (c > 22) return 0; 
	while (c--) x = x*5%mod; 
	for (ll i = n;i > n-m;i--) {
		k = i; while (k%5 == 0) k /= 5; 
		res = res*k%mod; 
	}
	for (ll i = 1;i <= m;i++) {
		k = i; while (k%5 == 0) k /= 5; 
		res = res*qpow(k)%mod; 
	}
	return res*x%mod; 
}
struct vc {
	LL f[25]; 
	void clr () { memset(f, 0, sizeof f); }
	friend vc operator + (const vc & a, const ll &b) {
		vc c; c.clr(); 
		for (int i = 0;i < 25;i++) {
			for (int j = 0;j <= i;j++) c.f[i-j] += a.f[i]*qpow(b, j)%mod*lC(i, j)%mod, c.f[i-j] %= mod;  
		}
		return c; 
	}
	friend vc operator * (const vc & a, const vc & b) {
		vc c; memset(c.f, 0, sizeof c.f); 
		for (int i = 0;i < 25;i++) {
			for (int j = 0;i+j < 25;j++) c.f[i+j] += a.f[i]*b.f[j]%mod, c.f[i+j] %= mod; 
		} 
		return c; 
	}
}dd;
void init () {
	dd.clr(); 
	for (int i = 0;i < 16;i++) {
		ll k = 1; 
		for (int j = 0;j < 4;j++) if (i>>j&1) k = k*(j+1); 
		dd.f[4-__builtin_popcount(i)] += k; 
	}
		
}

vc gv (ll n) {
	if (n == 0) return dd; 
	vc k = gv(n-1>>1); 
	vc res = k*(k+(((n-1)/2+1)*5%mod)); 
	if (n&1^1) res = res*(dd+(n*5%mod)); 
	return res; 
}

LL sc (ll n) {
	if (n < 0) return 1; 
	return gv(n).f[0]; 
}

LL fac (ll n) {
	if (n == 0) return 1; 
	LL res = 1; 
	for (ll i = n/5*5+1;i <= n;i++) res = res*i%mod; 
	res = res*fac(n/5)%mod*sc(n/5-1)%mod; 
	return res; 
}

ll C (ll n, ll m) {
	if (m > n) return 0; 
	if (m > n-m) m = n-m; 
	LL res = 1; 
	ll c = 0, x = 1; 
	LL k = n; while (k) c += k/5, k /= 5; 
	k = m; while (k) c -= k/5, k /= 5; 
	k = n-m; while (k) c -= k/5, k /= 5;
	if (c > 22) return 0; 
	while (c--) x = x*5%mod; 
	return fac(n)*qpow(fac(n-m)*fac(m)%mod)%mod*x%mod; 
}

void solve () {
	init(); 
	memset(f, -0x3f, sizeof f); 
	cin >> n >> m >> k >> M;
	for (int i = 1;i <= n;i++) cin >> w[i];
	for (int i = 1;i <= n;i++) cin >> v[i]; 
	for (int i = 1;i < n;i++) {
		int x, y; ll c; cin >> x >> y >> c; 
		e[x].pb({y, c}); e[y].pb({x, c});
	}
	for (int i = 1;i <= n;i++) dfs(i, i, 0); 
	for (int i = 1;i <= n;i++) dp(i, 0); 
	ll ans = -inf, cnt = 0; 
	for (int i = 1;i <= n;i++) for (int j = 0;j <= m;j++) if (f[i][0][j] > ans) ans = f[i][0][j]; //, cout << "DP:" << i << " " << j << " " << f[i][0][j] << endl; 
//	cout << ans << endl; 
	for (int i = 1;i <= n;i++) {
		memset(sk, 0, sizeof sk); 
		for (int j = 1;j <= n;j++) vis[j] = chk(i, j); //, cout << vis[j] << " "; cout << endl; 
		sk[i] = 1; dp1(i, 0); 
		ll sc = 0; 
		for (int j = 0;j <= m;j++) {
			if (fs[i][j].v == ans) sc += fs[i][j].c; 
		}
		cnt += C(sc, k), cnt %= mod; 
	}
	for (int i = 1;i <= n;i++) {
		for (auto j : e[i]) {
			if (j.fi > i) continue; 
			memset(sk, 0, sizeof sk); 
			for (int z = 1;z <= n;z++) vis[z] = chk(i, z) && chk(j.fi, z); 
			sk[i] = sk[j.fi] = 1; 
			dp1(i, j.fi); dp1(j.fi, i); 
			
			for (int z = 0;z <= m;z++) gs[z].clr(); 
			td.clear(); 
			for (int z = 0;z <= m;z++) if (fs[j.fi][z].v >= 0) td.pb(z); 
			for (int z = 0;z <= m;z++) {
				if (fs[i][z].v < 0) continue;
				for (int x : td) if (z+x <= m) gs[z+x] = gs[z+x]+(fs[i][z]*fs[j.fi][x]);  
			}
			ll sc = 0; 
			for (int z = 0;z <= m;z++) if (gs[z].v == ans) sc += gs[z].c; 
//			cout << i << " " << j.fi << " " << -sc << " " << C(sc, k) << endl; 
			cnt -= C(sc, k), cnt %= mod; 
		}
	}
	(cnt += mod) %= mod; 
	cout << cnt; 
}

signed main () {
//	freopen("t.out", "w", stdout); 
//	ios::sync_with_stdio(0);
//	cin.tie(0); cout.tie(0);
	int T = 1; 
	while (T--) solve();
	return 0;
}