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.IOException;
 import java.io.InputStream;
 import java.io.PrintWriter;
 import java.io.*;
 import java.util.*;
 import java.util.LinkedList;
 import java.math.*;
 import java.lang.*;
 import java.util.PriorityQueue;
 import static java.lang.Math.*;
 @SuppressWarnings("unchecked")
 public class Solution implements Runnable {
     static class InputReader {
         private InputStream stream;
         private byte[] buf = new byte[1024];
         private int curChar;
         private int numChars;
         private SpaceCharFilter filter;
         private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

         public InputReader(InputStream stream) {
             this.stream = stream;
         }

         public int read() {
             if (numChars==-1)
                 throw new InputMismatchException();

             if (curChar >= numChars) {
                 curChar = 0;
                 try {
                     numChars = stream.read(buf);
                 }
                 catch (IOException e) {
                     throw new InputMismatchException();
                 }

                 if(numChars <= 0)
                     return -1;
             }
             return buf[curChar++];
         }

         public String nextLine() {
             String str = "";
             try {
                 str = br.readLine();
             }
             catch (IOException e) {
                 e.printStackTrace();
             }
             return str;
         }
         public int nextInt() {
             int c = read();

             while(isSpaceChar(c))
                 c = read();

             int sgn = 1;

             if (c == '-') {
                 sgn = -1;
                 c = read();
             }

             int res = 0;
             do {
                 if(c<'0'||c>'9')
                     throw new InputMismatchException();
                 res *= 10;
                 res += c - '0';
                 c = read();
             }
             while (!isSpaceChar(c));

             return res * sgn;
         }

         public long nextLong() {
             int c = read();
             while (isSpaceChar(c))
                 c = read();
             int sgn = 1;
             if (c == '-') {
                 sgn = -1;
                 c = read();
             }
             long res = 0;

             do {
                 if (c < '0' || c > '9')
                     throw new InputMismatchException();
                 res *= 10;
                 res += c - '0';
                 c = read();
             }
             while (!isSpaceChar(c));
                 return res * sgn;
         }

         public double nextDouble() {
             int c = read();
             while (isSpaceChar(c))
                 c = read();
             int sgn = 1;
             if (c == '-') {
                 sgn = -1;
                 c = read();
             }
             double res = 0;
             while (!isSpaceChar(c) && c != '.') {
                 if (c == 'e' || c == 'E')
                     return res * Math.pow(10, nextInt());
                 if (c < '0' || c > '9')
                     throw new InputMismatchException();
                 res *= 10;
                 res += c - '0';
                 c = read();
             }
             if (c == '.') {
                 c = read();
                 double m = 1;
                 while (!isSpaceChar(c)) {
                     if (c == 'e' || c == 'E')
                         return res * Math.pow(10, nextInt());
                     if (c < '0' || c > '9')
                         throw new InputMismatchException();
                     m /= 10;
                     res += (c - '0') * m;
                     c = read();
                 }
             }
             return res * sgn;
         }

         public String readString() {
             int c = read();
             while (isSpaceChar(c))
                 c = read();
             StringBuilder res = new StringBuilder();
             do {
                 res.appendCodePoint(c);
                 c = read();
             }
             while (!isSpaceChar(c));

             return res.toString();
         }

         public boolean isSpaceChar(int c) {
             if (filter != null)
                 return filter.isSpaceChar(c);
             return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
         }

         public String next() {
             return readString();
         }

         public interface SpaceCharFilter {
             public boolean isSpaceChar(int ch);
         }
     }
     public static long min(long a,long b)
     {
         if(a>b)
         {
             return b;
         }
         return a;
     }
     public static int min(int a,int b)
     {
         if(a>b)
         {
             return b;
         }
         return a;
     }
     public static long max(long a,long b)
     {
         if(a>b)
         {
             return a;
         }
         return b;
     }
     public static int max(int a,int b)
     {
         if(a>b)
         {
             return a;
         }
         return b;
     }
     static class pair implements Comparable<pair>
     {
       int x;
       int y;
       pair(int x,int y)
       {
         this.x = x;
         this.y = y;
       }
       public int compareTo(pair p)
       {
         return this.x-p.x;
       }
     }
     public static int gcd(int a,int b)
     {
         if(a==0)
         return b;
         if(b==0)
         return a;
         while((a%=b)!=0&&(b%=a)!=0);
         return a^b;
     }
     public static int mod(int a)
     {
       if(a>0)
         return a;
       return -a;
     }
     static int mod = (int)1e9+7;
     public static long expo(long exp,long pow)
     {
       long ans = 1;
       while(pow!=0)
       {
         if((pow&1)==1)
         {
           ans = (ans*exp)%mod;
         }
         exp = (exp*exp)%mod;
         pow = pow>>1;
       }
       return ans;
     }
     static int max = (int)1e5;
     public static long fact(int num)
     {
         if(num==0)
         {
           return 1;
         }
         return (fact(num-1)*num)%mod;
     }
     static int[] sieve;
     public static void sieve()
     {
       sieve = new int[max];
       for(int i=1;i<max;i++)
       {
         sieve[i] = i;
       }
       for(int i=2;i<max;i++)
       {
         if(sieve[i]==i)
         {
           for(int j=i*2;j<max;j+=i)
           {
             if(sieve[j]==j)
             {
               sieve[j] = i;
             }
           }
         }
       }
     }
     public static int lcm(int a,int b)
     {
       return a*b/gcd(a,b);
     }
     public static int bsearch(pair[] p,int x)
     {
       int l = 0;
       int r = p.length-1;
       while(r>l)
       {
         int mid = (l+r)/2;
         if(p[mid].y<=x)
         {
           l = mid+1;
         }
         else if(p[mid].x>x)
         {
           r = mid;
         }
         else
         {
           return 0;
         }
       }
       if(x>=p[r].x&&x<p[r].y)
       {
         return 0;
       }
       return p[r].x-x;
     }
     static int[][] up;
     static long[][] sum;
     static int ans = 0;
     static int len;
     static int l;
     static int[] w;
     static long s;
     static ArrayList<Integer>[] list;
     public static int get(int v)
     {
       int h = 0;
       int sm = w[v];
       for(int i=l;i>=0;i--)
       {
         if(h+(1<<i)<len&&sum[v][i]+sm<=s)
         {
           h+=(1<<i);
           sm+=sum[v][i];
           v = up[v][i];
         }
       }
       return h;
     }
     public static int dfs(int v)
     {
       int mx = -1;
       for(Integer x:list[v])
       {
         mx = max(mx,dfs(x)-1);
       }
       if(mx==-1)
       {
         mx = get(v);
         ans++;
       }
       return mx;
     }
     public static void main(String args[]) throws Exception {
         new Thread(null, new Solution(),"Main",1<<26).start();
     }
     public void run() {
       InputReader sc  = new InputReader(System.in);
       PrintWriter out = new PrintWriter(System.out);
       int t1 = 1;
       while(t1-->0)
       {
         int n = sc.nextInt();
         len = sc.nextInt();
         s = sc.nextLong();
         w = new int[n];
         int[] p = new int[n];
         list = new ArrayList[n];
         for(int i=0;i<n;i++)
         {
           w[i] = sc.nextInt();
           if(w[i]>s)
           {
             out.println(-1);
             out.close();
             return;
           }
           list[i] = new ArrayList<>();
         }
         for(int i=1;i<n;i++)
         {
           p[i] = sc.nextInt()-1;
           list[p[i]].add(i);
         }
         l = 0;
         while((1<<l)<n)l++;
         up = new int[n][l+1];
         sum = new long[n][l+1];
         for(int i=0;i<n;i++)
         {
           up[i][0] = p[i];
           sum[i][0] = w[p[i]];
         }
         for(int i=0;i<n;i++)
         {
           for(int j=1;j<=l;j++)
           {
             up[i][j] = up[up[i][j-1]][j-1];
             sum[i][j] = sum[i][j-1]+sum[up[i][j-1]][j-1];
           }
         }
         dfs(0);
         out.println(ans);
       }
      out.close();
   }
 }
