#include <cstdio>
#include <iostream>
#include <array>
using namespace std;
#define int long long
#define ll __int128
const int M = 105;
const int p = 11920928955078125;
int read()
{
	int x=0,f=1;char c;
	while((c=getchar())<'0' || c>'9') {if(c=='-') f=-1;}
	while(c>='0' && c<='9') {x=(x<<3)+(x<<1)+(c^48);c=getchar();}
	return x*f;
}
int n,m,k,t,mx,ans,tot,f[M],a[M],w[M],ok[M];
int cnt,id[M],dfn[M],out[M],C[30][30];
struct node{int x,y;}dp[M][10005];
struct edge{int v,c,next;}e[M<<1];
void pre(int u,int fa,int d,int &s)
{
	if((ll)a[u]*d<=t) s|=(1ll<<u);
	for(int i=f[u];i;i=e[i].next)
		if(e[i].v^fa) pre(e[i].v,u,d+e[i].c,s);
}
void dfs(int u,int fa)
{
	dfn[u]=++cnt;id[cnt]=u;
	for(int i=f[u];i;i=e[i].next)
		if(e[i].v^fa) dfs(e[i].v,u);
	out[dfn[u]]=cnt;
}
void trans(node &a,node b,int c)
{
	if(!b.y) return ;//important judge
	if(a.x<b.x+c) a.x=b.x+c,a.y=0;
	if(a.x==b.x+c) a.y+=b.y;
}
void work(int s,int u,int v)
{
	cnt=0;dfs(u,0);
	for(int i=0;i<=n;i++)
		for(int j=0;j<=m;j++)
			dp[i][j].x=dp[i][j].y=0;
	for(int i=0;i<=m;i++) dp[0][i].y=1;
	for(int i=1;i<=n;i++)
	{
		int u=id[i];//choose i
		if(s>>u&1) for(int j=m;j>=w[u];j--)
			trans(dp[i][j],dp[i-1][j-w[u]],a[u]);
		if(i>1 && (dfn[v]<i || dfn[v]>out[i]))
			for(int j=0;j<=m;j++)
				trans(dp[out[i]][j],dp[i-1][j],0); 
	}
}
int count(int n)
{
	int res=0;while(n) res+=n/=5;
	return res;
}
array<ll,25> zxy(int n)
{
	ll a[25]={},b[25]={};b[0]=1;array<ll,25> res;
	if(n==0) {res.fill(0);res[0]=1;return res;}
	int tn=n/10*5;res=zxy(tn);
	for(int i=1;i<23;i++) b[i]=b[i-1]*tn%p;
	//binomial theorem
	for(int i=0;i<23;i++)
		for(int j=i;j<23;j++)
			a[i]=(a[i]+res[j]*C[j][j-i]%p*b[j-i])%p;
	//convolution
	for(int i=22;i>=0;i--)
	{
		ll t=0;
		for(int j=0;j<=i;j++)
			t=(t+res[j]*a[i-j])%p;
		res[i]=t;
	}
	//some remaining numbers
	for(;n>2*tn;n--) if(n%5)
		for(int i=22;i>=0;i--)
			res[i]=(res[i]*n+(i?res[i-1]:0))%p;
	return res;
}
ll fac(int n)
{
	ll res=1;
	while(n) res=res*zxy(n)[0]%p,n/=5;
	return res;
}
void exgcd(int a,int b,int &x,int &y)
{
	if(!b) {x=1;y=0;return ;}
	exgcd(b,a%b,y,x);y-=(a/b)*x;
}
int comb(int n)
{
	if(n<k) return 0;
	int d=count(n)-count(k)-count(n-k);
	int t=fac(n-k)*fac(k)%p,x=0,y=0;
	exgcd(t,p,x,y);x=(x%p+p)%p;
	x=x*fac(n)%p;
	while(d--) x=x*5%p;
	return x;
}
void calc(int u,int fa)
{
	work(ok[u],u,0);
	if(dp[n][m].x==mx)
		ans=(ans+comb(dp[n][m].y))%p;
	for(int i=f[u];i;i=e[i].next)
	{
		int v=e[i].v;
		if(v==fa) continue;
		calc(v,u);
		work(ok[u]&ok[v],u,v);
		if(dp[n][m].x==mx)
			ans=(ans-comb(dp[n][m].y))%p;
	}
}
signed main()
{
	n=read();m=read();k=read();t=read();
	for(int i=1;i<=n;i++) w[i]=read();
	for(int i=1;i<=n;i++) a[i]=read();
	for(int i=1;i<n;i++)
	{
		int u=read(),v=read(),c=read();
		e[++tot]=edge{v,c,f[u]},f[u]=tot;
		e[++tot]=edge{u,c,f[v]},f[v]=tot;
	}
	for(int i=1;i<=n;i++) pre(i,0,0,ok[i]);
	for(int i=1;i<=n;i++)
		work((1ll<<n+1)-1,i,0),mx=max(mx,dp[n][m].x);
	for(int i=0;i<=22;i++)
	{
		C[i][0]=1;
		for(int j=1;j<=i;j++)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%p;
	}
	calc(1,0);
	printf("%lld\n",(ans%p+p)%p);
}