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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * @author Don Li
 */
public class SplitTheTree {
    
    int N = (int) 1e5 + 10;
    int LOG = 18;
    
    int[] dep = new int[N];        
    long[] sum = new long[N];      
    int[][] anc = new int[N][LOG]; 
    int[] up = new int[N];         
    
    int[][] G;
    
    void solve() {
        int n = in.nextInt(), L = in.nextInt(); long S = in.nextLong();
        int[] w = new int[n];
        for (int i = 0; i < n; i++) w[i] = in.nextInt();
        int[] p = new int[n];
        p[0] = -1;
        for (int i = 1; i < n; i++) p[i] = in.nextInt() - 1;
        
        int[] fr = new int[n - 1], to = new int[n - 1];
        for (int i = 0; i < n - 1; i++) {
            fr[i] = i + 1;
            to[i] = p[i + 1];
        }
        G = build_graph(n, fr, to);
        
        for (int i = 0; i < n; i++) {
            if (w[i] > S) {
                out.println(-1);
                return;
            }
        }
        
        dep[0] = 0;
        sum[0] = w[0];
        for (int i = 1; i < n; i++) {
            dep[i] = dep[p[i]] + 1;
            sum[i] = w[i] + sum[p[i]];
        }
        
        anc[0][0] = 0;
        for (int i = 1; i < n; i++) {
            anc[i][0] = p[i];
            for (int j = 1; j < LOG; j++) anc[i][j] = anc[anc[i][j - 1]][j - 1];
        }
        
        for (int i = 0; i < n; i++) {
            int v = i, dist = L - 1;
            for (int j = LOG - 1; j >= 0; j--) {
                if (1 << j <= dist && sum[i] - sum[anc[v][j]] + w[anc[v][j]] <= S) {
                    dist -= 1 << j;
                    v = anc[v][j];
                }
            }
            up[i] = v;
        }
        
        int[] dp = new int[n];
        int[] hi = new int[n];
        for (int i = n - 1; i >= 0; i--) {
            int best = -1;
            for (int j : G[i]) {
                if (j != p[i]) {
                    dp[i] += dp[j];
                    if (hi[j] == j) continue;
                    if (best < 0 || dep[best] > dep[hi[j]]) best = hi[j];
                }
            }
            if (best < 0) {
                dp[i]++;
                best = up[i];
            }
            hi[i] = best;
        }
        out.println(dp[0]);
    }
    
    int[][] build_graph(int n, int[] from, int[] to) {
        int[][] G = new int[n][];
        int[] cnt = new int[n];
        for (int i = 0; i < from.length; i++) {
            cnt[from[i]]++;
            cnt[to[i]]++;
        }
        for (int i = 0; i < n; i++) G[i] = new int[cnt[i]];
        for (int i = 0; i < from.length; i++) {
            G[from[i]][--cnt[from[i]]] = to[i];
            G[to[i]][--cnt[to[i]]] = from[i];
        }
        return G;
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new SplitTheTree().solve();
        out.close();
    }
    
    static FastScanner in;
    static PrintWriter out;
    
    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;
        
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
        
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
        
        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
