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;
vector<int> v[100010];
int cnt, i, j, x, y, n, l, depth[100010], dyn[100010], fat[100010][25];
long long s, w[100010], part[100010];
int findw(int poz, long long s) {
  if (poz == 1) return 1;
  if (w[poz] + w[fat[poz][0]] > s) return poz;
  for (j = 1; j <= 20; j++)
    if (((part[poz] - part[fat[fat[poz][j]][0]]) >= s) || (!fat[poz][j]))
      return findw(fat[poz][j - 1], s - (part[poz] - part[fat[poz][j - 1]]));
}
int main() {
  cin >> n >> l >> s;
  for (i = 1; i <= n; i++) {
    cin >> w[i];
    if (w[i] > s) {
      cout << -1;
      return 0;
    }
  }
  part[1] = w[1];
  fat[1][0] = 0;
  for (i = 2; i <= n; i++) {
    cin >> fat[i][0];
    part[i] = part[fat[i][0]] + w[i];
    depth[i] = depth[fat[i][0]] + 1;
  }
  for (i = 1; i <= n; i++)
    for (j = 1; j <= 20; j++) fat[i][j] = fat[fat[i][j - 1]][j - 1];
  for (i = n; i >= 1; i--) {
    if (!dyn[i]) dyn[i] = min(depth[i] - depth[findw(i, s)] + 1, l), cnt++;
    dyn[fat[i][0]] = max(dyn[fat[i][0]], dyn[i] - 1);
  }
  cout << cnt;
  return 0;
}
