You are given a rooted tree on n vertices, its root is the vertex number 1. The i-th vertex contains a number w_i. Split it into the minimum possible number of vertical paths in such a way that each path contains no more than L vertices and the sum of integers w_i on each path does not exceed S. Each vertex should belong to exactly one path.

A vertical path is a sequence of vertices v_1, v_2, …, v_k where v_i (i ≥ 2) is the parent of v_{i - 1}.

Input

The first line contains three integers n, L, S (1 ≤ n ≤ 10^5, 1 ≤ L ≤ 10^5, 1 ≤ S ≤ 10^{18}) — the number of vertices, the maximum number of vertices in one path and the maximum sum in one path.

The second line contains n integers w_1, w_2, …, w_n (1 ≤ w_i ≤ 10^9) — the numbers in the vertices of the tree.

The third line contains n - 1 integers p_2, …, p_n (1 ≤ p_i < i), where p_i is the parent of the i-th vertex in the tree.

Output

Output one number — the minimum number of vertical paths. If it is impossible to split the tree, output -1.

Examples

Input

3 1 3
1 2 3
1 1


Output

3

Input

3 3 6
1 2 3
1 1


Output

2

Input

1 1 10000
10001


Output

-1

Note

In the first sample the tree is split into \{1\},\ \{2\},\ \{3\}.

In the second sample the tree is split into \{1,\ 2\},\ \{3\} or \{1,\ 3\},\ \{2\}.

In the third sample it is impossible to split the tree.
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 7;
const int mod = 1e9 + 7;
int n, L, ans;
long long S;
int w[maxn];
int up[maxn], down[maxn];
int f[maxn][20], dep[maxn];
long long sum[maxn];
vector<int> g[maxn];
void dfs(int u, int fa) {
  dep[u] = dep[fa] + 1;
  sum[u] = sum[fa] + w[u];
  up[u] = u;
  f[u][0] = fa;
  for (int j = 1; (1 << j) <= dep[u]; j++) f[u][j] = f[f[u][j - 1]][j - 1];
  int num = L;
  for (int i = 19; i >= 0; i--) {
    int no = f[up[u]][i];
    if (!no || (1 << i) >= num) continue;
    if (sum[u] - sum[no] + w[no] > S) continue;
    num -= (1 << i);
    up[u] = no;
  }
  for (auto v : g[u]) {
    if (v != fa) dfs(v, u);
  }
}
void _dfs(int u, int fa) {
  int best = -1;
  for (auto v : g[u]) {
    if (v == fa) continue;
    _dfs(v, u);
    if (down[v] == v) continue;
    if (best == -1 || dep[best] > dep[down[v]]) {
      best = down[v];
    }
  }
  if (best == -1) {
    best = up[u];
    ans++;
  }
  down[u] = best;
}
int main() {
  cin >> n >> L >> S;
  int ma = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &w[i]);
    ma = max(ma, w[i]);
  }
  for (int u = 2, v; u <= n; u++) {
    scanf("%d", &v);
    g[u].push_back(v);
    g[v].push_back(u);
  }
  if (ma > S) {
    puts("-1");
    return 0;
  }
  dfs(1, 0);
  ans = 0;
  _dfs(1, 0);
  cout << ans << '\n';
  return 0;
}
