#include <bits/stdc++.h>
const int N = 5e4 + 5;
std::vector<std::pair<int, int> > op[N];
double ans[N];
int c[N], n, m, q, C, cnt, nxt[N], head[N], to[N], a[N];
long long sum[N << 2] = {}, add[N << 2] = {}, sum2[N << 2] = {};
void change(int k, long long v, int len) {
  sum2[k] += 2 * sum[k] * v + v * v * len;
  sum[k] += v * len;
  add[k] += v;
}
void pushUp(int k) {
  sum[k] = sum[k << 1] + sum[k << 1 | 1];
  sum2[k] = sum2[k << 1] + sum2[k << 1 | 1];
}
void pushDown(int k, int l, int r) {
  if (!add[k]) return;
  change(k << 1, add[k], l);
  change(k << 1 | 1, add[k], r);
  add[k] = 0;
}
void update(int k, int lef, int rig, int l, int r, long long v) {
  if (l <= lef && rig <= r) {
    change(k, v, rig - lef + 1);
    return;
  }
  int mid = (lef + rig) >> 1;
  pushDown(k, mid - lef + 1, rig - mid);
  if (l <= mid) update(k << 1, lef, mid, l, r, v);
  if (r > mid) update(k << 1 | 1, mid + 1, rig, l, r, v);
  pushUp(k);
}
void init() {
  for (int i = 1; i <= n; i++) head[i] = -1;
  cnt = 0;
}
void addEdge(int u, int v) {
  to[cnt] = v;
  nxt[cnt] = head[u];
  head[u] = cnt++;
}
int dfn[N], top[N], size[N], par[N], ms[N], tot;
void dfs1(int u) {
  size[u] = 1;
  ms[u] = 0;
  for (int i = head[u]; ~i; i = nxt[i]) {
    int v = to[i];
    dfs1(v);
    size[u] += size[v];
    if (!ms[u] || size[ms[u]] < size[v]) ms[u] = v;
  }
}
void dfs2(int u, int tn) {
  top[u] = tn;
  dfn[u] = ++tot;
  if (ms[u]) dfs2(ms[u], tn);
  for (int i = head[u]; ~i; i = nxt[i]) {
    int v = to[i];
    if (v == ms[u]) continue;
    dfs2(v, v);
  }
}
void modify(int u, long long v) {
  int tp = top[u];
  while (u) update(1, 1, n, dfn[tp], dfn[u], v), u = par[tp], tp = top[u];
}
int main() {
  scanf("%d%d%d%d", &n, &m, &q, &C);
  int t, x, w, k;
  for (int i = 1; i <= n; i++)
    scanf("%d", a + i), op[a[i]].push_back(std::pair<int, int>(i, 1));
  init();
  for (int i = 2; i <= n; i++) scanf("%d", par + i), addEdge(par[i], i);
  for (int i = 1; i <= m; i++) scanf("%d", c + i);
  int num = 0;
  dfs1(1);
  dfs2(1, 1);
  while (q--) {
    scanf("%d", &t);
    if (t == 1)
      scanf("%d%d", &x, &w), op[a[x]].push_back(std::pair<int, int>(x, -1)),
          op[w].push_back(std::pair<int, int>(x, 1)), a[x] = w;
    else
      scanf("%d", &k), op[k].push_back(std::pair<int, int>(0, ++num));
  }
  if (!num) return 0;
  for (int i = 1; i <= m; i++) {
    for (int j = 0; j < op[i].size(); j++) {
      std::pair<int, int> now = op[i][j];
      if (!now.first)
        ans[now.second] = (1.0 * sum2[1] - 2.0 * C * sum[1]) / n + 1.0 * C * C;
      else
        modify(now.first, now.second * c[i]);
    }
    for (int j = op[i].size() - 1; ~j; j--) {
      std::pair<int, int> now = op[i][j];
      if (now.first) modify(now.first, -now.second * c[i]);
    }
  }
  for (int i = 1; i <= num; i++) printf("%.10f\n", ans[i]);
  return 0;
}
