#include <bits/stdc++.h>
#define rep(i,j,k) for(int i=(j);i<=(k);i++)
#define per(i,j,k) for(int i=(j);i>=(k);i--)
#define uint unsigned int
#define ll long long
#define ull unsigned long long
#define db double
#define ldb long double
#define pii pair<int,int>
#define pll pair<ll,ll>
#define mkp make_pair
#define eb emplace_back
#define SZ(S) (int)S.size()
//#define mod 998244353
#define mod 11920928955078125
#define inf 0x3f3f3f3f
#define linf 0x3f3f3f3f3f3f3f3f
using namespace std;

template <class T>
void chkmax(T &x,T y){
	if(x < y) x = y;
}

template <class T>
void chkmin(T &x,T y){
	if(x > y) x = y;
}

inline int popcnt(int x){
	return __builtin_popcount(x);
}

inline int ctz(int x){
	return __builtin_ctz(x);
}

int n,m;
ll K,MAX;
int W[65],Val[65];
int _u[65],_v[65],_w[65];

int cnt;
int head[65];
struct eg{
	int to,nxt,w;
}edge[125];

void make(int u,int v,int w){
	edge[++cnt].w = w;
	edge[cnt].to = v;
	edge[cnt].nxt = head[u];
	head[u] = cnt;
}

int dis[65][65];
void dfs(int u,int f,int s){
	for(int i = head[u];i;i = edge[i].nxt){
		int v = edge[i].to;
		if(v == f) continue;
		dis[s][v] = dis[s][u] + edge[i].w;
		dfs(v,u,s);
	}
}
pll dp[65][10005];
pll operator +(pll p,pll q){
	pll ret;
	ret = mkp(max(p.first,q.first),0);
	if(p.first == ret.first) ret.second += p.second;
	if(q.first == ret.first) ret.second += q.second;
	return ret;
}

int _ok[65];
void dfs(int u,int f){
	per(i,m,W[u]) dp[u][i] = mkp(dp[u][i - W[u]].first + Val[u],dp[u][i - W[u]].second);
	rep(i,0,W[u] - 1) dp[u][i] = mkp(-linf,0);

	if(!_ok[u]) rep(i,0,m) dp[u][i] = mkp(-linf,0);

	for(int i = head[u];i;i = edge[i].nxt){
		int v = edge[i].to;
		if(v == f) continue;
		rep(k,0,m) dp[v][k] = dp[u][k];
		dfs(v,u);
		rep(k,0,m) dp[u][k] = dp[u][k] + dp[v][k];
	}
}

template <class ADD>
inline void add(ADD &x,ADD y){
	x += y;
	if(x >= mod) x -= mod;
}

template <class SUB>
inline void sub(SUB &x,SUB y){
	x -= y;
	if(x < 0) x += mod;
}
#define lll __int128
ll power(ll p,ll _k = 9536743164062499ll){
	ll ans = 1;
	while(_k){
		if(_k % 2 == 1) ans = (lll)ans * p % mod;
		p = (lll)p * p % mod;
		_k /= 2;
	}
	return ans;
}

const int deg = 22;
struct poly{
	ll val[25];//0~22 次
}P[65],__;

poly operator *(poly p,poly q){
	poly c;
	fill(c.val,c.val + deg + 1,0);
	rep(i,0,deg){
		rep(j,0,deg - i) c.val[i + j] += (lll)p.val[i] * q.val[j] % mod;
	}
	rep(i,0,deg) c.val[i] %= mod;
	return c;
}

ll _tmp[25],C[25][25];
poly Delta(poly &p,ll N){//展开 (x+N)
	poly c;
	fill(c.val,c.val + deg + 1,0);

	_tmp[0] = 1;
	rep(i,1,deg) _tmp[i] = (lll)_tmp[i - 1] * N % mod;
	rep(i,0,deg){
		rep(j,0,i) c.val[j] += (lll)p.val[i] * C[i][j] % mod * _tmp[i - j] % mod;
	}
	rep(i,0,deg) c.val[i] %= mod;
	return c;
}

ll getval(poly &p,ll N){
	assert(N % 5 == 0);
	ll ans = 0,prd = 1;
	rep(i,0,deg){
		ans += (lll)prd * p.val[i] % mod;
		prd = (lll)prd * N % mod;
	}
	return ans % mod;
}

void init(){
	P[0].val[0] = 24;
	P[0].val[1] = 50;
	P[0].val[2] = 35;
	P[0].val[3] = 10;
	P[0].val[4] = 1;
	rep(k,1,60){
		P[k] = P[k - 1] * Delta(P[k - 1],5ll << (k - 1));
	}
}

ll getprd(ll N){//0~N 除了 5 倍数之外项的乘积.
	ll ret = 1;
	while(N >= 0 && N % 5 != 4){
		if(N % 5) ret = (lll)ret * N % mod;
		N--;
	}
	if(N < 0) return ret;

	N = N / 5 + 1;
	ll cur = 0;
	per(k,59,0){
		if(N >= (1ll << k)){
			ret = (lll)ret * getval(P[k],5 * cur) % mod;
			cur += 1ll << k;
			N -= 1ll << k;
		}
	}
	return ret;
}

/*ll bruteprd(ll N){
	ll ret = 1;
	rep(i,0,N) if(i % 5) ret = (lll)ret * i % mod;
	return ret;
}*/

pll Calc(ll N){//多少个因子 5,除去因子 5 之外.
//	printf("Calc %lld ",N);
	ll sum = 0,prd = 1;//,prd2 = bruteprd(N);
	while(N){
		sum += N / 5;
		prd = (lll)prd * getprd(N) % mod;
		N /= 5;
	}
//	printf("sum=%lld prd=%lld prd2=%lld\n",sum,prd,prd2);
	return mkp(sum,prd);
}

ll calc(ll N){//计算 C(N,K)
	if(N < K) return 0;
//	printf("ccalc %lld\n",N);
	pll tmp = Calc(N);
	ll sum = tmp.first,prd = tmp.second;
	tmp = Calc(K);
	sum -= tmp.first;prd = (lll)prd * power(tmp.second) % mod;
	tmp = Calc(N - K);
	sum -= tmp.first;prd = (lll)prd * power(tmp.second) % mod;
	return (lll)prd * power(5,min(sum,23ll)) % mod;
}

int main(){
//	freopen("test.in","r",stdin);
	rep(i,0,deg){
		C[i][0] = 1;
		rep(j,1,i) C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
	}
	init();
/*	ll awa;
	scanf("%lld%lld",&awa,&K);
	printf("%lld\n",calc(awa));
	return 0;*/
	scanf("%d%d%lld%lld",&n,&m,&K,&MAX);
	rep(u,1,n) scanf("%d",&W[u]);
	rep(u,1,n) scanf("%d",&Val[u]);
	rep(i,1,n - 1){
		scanf("%d%d%d",&_u[i],&_v[i],&_w[i]);
		make(_u[i],_v[i],_w[i]);make(_v[i],_u[i],_w[i]);
	}
	rep(u,1,n) dfs(u,0,u);

	ll ret = -1,ans = 0,qwq;
	rep(u,1,n){
		rep(v,1,n) _ok[v] = (1ll * dis[u][v] * Val[v] <= MAX);

		rep(k,0,m) dp[u][k] = mkp(-1,0);
		dp[u][0] = mkp(0,1);
		dfs(u,0);

		qwq = 0;
		rep(k,0,m){
			if(ret < dp[u][k].first){
				ret = dp[u][k].first;
				ans = 0;
				qwq = dp[u][k].second;
			}else if(ret == dp[u][k].first){
				qwq += dp[u][k].second;
			}
		}
		add(ans,calc(qwq));
	}

	rep(i,1,n - 1){
		rep(u,1,n) _ok[u] = (1ll * max(dis[u][_u[i]],dis[u][_v[i]]) * Val[u] <= MAX);
		rep(k,0,m) dp[_u[i]][k] = mkp(-1,0);
		dp[_u[i]][0] = mkp(0,1);
		dfs(_u[i],_v[i]);
		rep(k,0,m) dp[_v[i]][k] = dp[_u[i]][k];
		dfs(_v[i],_u[i]);

		qwq = 0;
		rep(k,0,m) if(ret == dp[_v[i]][k].first) qwq += dp[_v[i]][k].second;
		sub(ans,calc(qwq));
	}
	if(ret != -1) printf("%lld\n",ans);
	else printf("0\n");
	return 0;
}