#include <bits/stdc++.h>
using namespace std;
#define maxn 3000000
#define int long long
#define db double
int n, m, q, C, cnt, f[maxn], co[maxn], dfn[maxn];
int size[maxn], hson[maxn], top[maxn], fa[maxn];
int root[maxn], mark[maxn * 2], cal[maxn * 2], cal2[maxn * 2], son[maxn * 2][2];int read()
{int x = 0, k = 1;char c; c = getchar();while(c < '0' || c > '9') { if(c == '-') k = -1; c = getchar(); }while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();return x * k;
}struct edge
{int cnp, to[maxn], last[maxn], head[maxn];edge() { cnp = 2; }void add(int u, int v){ to[cnp] = v, last[cnp] = head[u], head[u] = cnp ++; }
}E1;void dfs(int u)
{size[u] = 1; int mx = 0, hs = 0;for(int i = E1.head[u]; i; i = E1.last[i]){int v = E1.to[i];fa[v] = u; dfs(v); size[u] += size[v];if(size[v] >= mx) mx = size[v], hs = v;}hson[u] = hs;
}void dfs2(int u, int anc)
{dfn[u] = ++ cnt, top[u] = anc;if(hson[u]) dfs2(hson[u], anc);for(int i = E1.head[u]; i; i = E1.last[i])if(E1.to[i] != hson[u]) dfs2(E1.to[i], E1.to[i]);
}void Add(int &p, int l, int r, int x)
{if(!p) p = ++ cnt; mark[p] += x;cal2[p] += cal[p] * x + (r - l + 1) * x * x; cal[p] += (r - l + 1) * x * 2;
}void Push_down(int p, int l, int r)
{int mid = (l + r) >> 1;if(!mark[p]) return;Add(son[p][0], l, mid, mark[p]); Add(son[p][1], mid + 1, r, mark[p]);mark[p] = 0;
}void Push_Up(int p)
{int l = son[p][0], r = son[p][1];cal2[p] = cal2[l] + cal2[r]; cal[p] = cal[l] + cal[r];
}void Update(int &p, int l, int r, int L, int R, int x)
{if(L > R || l > r) return;if(!p) p = ++ cnt;if(L <= l && R >= r) { Add(p, l, r, x); return; }Push_down(p, l, r); int mid = (l + r) >> 1;if(L <= mid) Update(son[p][0], l, mid, L, R, x); if(R > mid) Update(son[p][1], mid + 1, r, L, R, x);Push_Up(p);
}void T_Update(int k, int u, int x)
{for(; u; u = fa[top[u]])Update(root[k], 1, n, dfn[top[u]], dfn[u], x);
}int Cal(int p)
{ return co[p] * co[p] * cal2[root[p]] - cal[root[p]] * C * co[p] + n * C * C; }signed main()
{n = read(), m = read(), q = read(), C = read();for(int i = 1; i <= n; i ++) f[i] = read();for(int i = 2; i <= n; i ++) { int x = read(); E1.add(x, i); }for(int i = 1; i <= m; i ++) co[i] = read();dfs(1), dfs2(1, 1), cnt = m;for(int i = 1; i <= m; i ++) root[i] = i;for(int i = 1; i <= n; i ++) T_Update(f[i], i, 1);for(int i = 1; i <= q; i ++){int opt = read();if(opt == 1) {int x = read(), k = read();T_Update(f[x], x, -1), T_Update(f[x] = k, x, 1); }else {int k = read();printf("%lf\n", (db) Cal(k) / (db) n);}}return 0;
}