//https://oj.uz/problem/view/APIO16_fireworks
//Solution by Mikołaj Kołek
#include "bits/stdc++.h"
#define intin *istream_iterator<int>(cin)
using namespace std;
struct Node {
long long parentConnectionLength = 0, largestChild = -1;
bool isExplosive = false;
vector<int> children;
};
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n = intin, m = intin;
vector<Node> G(n + m);
for(int i = 1; i < (n + m); i++) {
G[intin - 1].children.push_back(i);
G[i].parentConnectionLength = intin;
G[i].isExplosive = (i >= n);
}
function<int(int)> DFS1 = [&] (int v) {
int maxChildSize = -1, mySize = 1;
for(int i = 0; i < G[v].children.size(); i++) {
int childSize = DFS1(G[v].children[i]);
mySize += childSize;
if(childSize > maxChildSize) {
maxChildSize = childSize;
G[v].largestChild = i;
}
}
return mySize;
};
DFS1(0);
function <long long(int, priority_queue<int>&)> DFS2 = [&] (int v, priority_queue<int> &Q) {
if(G[v].isExplosive) {
Q.push(G[v].parentConnectionLength);
Q.push(G[v].parentConnectionLength);
return -G[v].parentConnectionLength;
}
long long b = DFS2(G[v].children[G[v].largestChild], Q);
for(int i = 0; i < G[v].children.size(); i++) {
if(i == G[v].largestChild)
continue;
priority_queue<int> Q2;
b += DFS2(G[v].children[i], Q2);
while(!Q2.empty()) {
Q.push(Q2.top());
Q2.pop();
}
}
for(int i = 0; i < (G[v].children.size() - ((v != 0) ? 1 : 0)); i++) {
b += Q.top();
Q.pop();
}
if(!Q.empty()) {
int top = Q.top(); Q.pop();
if(!Q.empty()) {
int top2 = Q.top(); Q.pop();
Q.push(top2 + G[v].parentConnectionLength);
}
Q.push(top + G[v].parentConnectionLength);
}
return b - G[v].parentConnectionLength;
};
priority_queue<int> Q;
cout << DFS2(0, Q);
return 0;
}
