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| #include<bits/stdc++.h>
#define SIZE 250
#define ll long long
#define INF 2147483647
#define is_bad(a, m, c) ((m.b - c.b) * (m.k - a.k) <= (a.b - m.b) * (c.k - m.k))
int inp(){
char c = getchar();
int neg = 1;
while(c < '0' || c > '9'){
if(c == '-')
neg = -1;
c = getchar();
}
int sum = 0;
while(c >= '0' && c <= '9'){
sum = sum * 10 + c - '0';
c = getchar();
}
return sum * neg;
}
int head[200010], nxt[200010], end[200010], dfn[200010], size[200010];
ll a2[200010], b2[200010], a[200010], b[200010];
int cou = 0;
void link(int a, int b){
nxt[++cou] = head[a];
head[a] = cou;
end[cou] = b;
}
struct Node{
ll k;
ll b;
ll get(int x){
return x * k + b;
}
};
bool cmp(Node a, Node b){
return a.k < b.k;
}
struct Convex{
std::vector<Node> s;
void insert(Node x){
while(s.size() > 1 && is_bad(s[s.size() - 2], s[s.size() - 1], x))
s.resize(s.size() - 1);
s.push_back(x);
}
ll query(ll x){
if(s.size() == 0)
return -1e18;
int l = 0;
int r = s.size() - 1;
while(l < r){
int mid = (l + r) >> 1;
if(s[mid].get(x) <= s[mid + 1].get(x))
l = mid + 1;
else
r = mid;
}
return s[l].get(x);
}
void clear(){
s.clear();
}
}c[1000], cf[1000];
int ql[1000], qr[1000];
ll delta[1000];
std::vector<Node> vec;
void rebuild(int x){
vec.clear();
c[x].clear();
cf[x].clear();
for(int i = ql[x]; i <= qr[x]; i++){
a[i] += delta[x];
vec.push_back((Node){b[i], a[i] * b[i]});
}
std::sort(vec.begin(), vec.end(), cmp);
for(int i = 0; i < vec.size(); i++)
c[x].insert(vec[i]);
for(int i = 0; i < vec.size(); i++)
cf[x].insert((Node){vec[i].k, -vec[i].b});
delta[x] = 0;
}
int idx = 0;
void dfs(int cur){
dfn[cur] = ++idx;
size[cur] = 1;
for(int x = head[cur]; x != -1; x = nxt[x]){
a[end[x]] += a[cur];
b[end[x]] += b[cur];
dfs(end[x]);
size[cur] += size[end[x]];
}
}
int main(){
memset(head, -1, sizeof(head));
int n = inp();
int q = inp();
for(int i = 2; i <= n; i++){
int fa = inp();
link(fa, i);
}
for(int i = 1; i <= n; i++)
a[i] = inp();
for(int i = 1; i <= n; i++)
b[i] = inp();
dfs(1);
memcpy(a2, a, sizeof(a));
memcpy(b2, b, sizeof(b));
for(int i = 1; i <= n; i++){
a[dfn[i]] = a2[i];
b[dfn[i]] = abs(b2[i]);
}
qr[0] = 0;
int cur = 1;
while(qr[cur - 1] < n){
ql[cur] = qr[cur - 1] + 1;
qr[cur] = ql[cur] + SIZE - 1;
cur++;
}
qr[cur - 1] = n;
for(int i = 1; i < cur; i++)
rebuild(i);
while(q--){
int op = inp();
if(op == 1){
int v = inp();
ll x = inp();
int l = dfn[v];
int r = dfn[v] + size[v] - 1;
int lb = (l - 1) / SIZE + 1;
int rb = (r - 1) / SIZE + 1;
if(lb == rb){
for(int i = l; i <= r; i++)
a[i] += x;
rebuild(lb);
} else {
for(int i = lb + 1; i < rb; i++)
delta[i] += x;
for(int i = l; i <= qr[lb]; i++)
a[i] += x;
for(int i = ql[rb]; i <= r; i++)
a[i] += x;
rebuild(lb);
rebuild(rb);
}
} else {
int v = inp();
int l = dfn[v];
int r = dfn[v] + size[v] - 1;
int lb = (l - 1) / SIZE + 1;
int rb = (r - 1) / SIZE + 1;
ll ans = -1e18;
if(lb == rb){
for(int i = l; i <= r; i++)
ans = std::max(ans, abs(a[i] + delta[lb]) * b[i]);
} else {
for(int i = lb + 1; i < rb; i++){
ans = std::max(ans, c[i].query(delta[i]));
ans = std::max(ans, cf[i].query(-delta[i]));
}
for(int i = l; i <= qr[lb]; i++)
ans = std::max(ans, abs(a[i] + delta[lb]) * b[i]);
for(int i = ql[rb]; i <= r; i++)
ans = std::max(ans, abs(a[i] + delta[rb]) * b[i]);
}
printf("%lld\n", ans);
}
}
}
|
