CF 966E May Holidays

/*
考虑对于询问分块, 每根号n个询问做一次
考虑一次询问, 我们建立出虚树来每条链上的更改一定是一样的, 然后会有根号条链

对于每条链上的点按照w基数排序并且合并相同, 然后每次更改 就是一个指针移动一格, 根号n次更改每次都要枚举一遍所有的链 所以是On的

总体N\sqrt(N)

比着 DOFYPXY 的代码打的
*/
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<queue>
#include<cmath>
#define ll long long
#define M 100010
#define mmp make_pair
using namespace std;
int read() {
	int nm = 0;
	char c = getchar();
	for(; !isdigit(c); c = getchar());
	for(; isdigit(c); c = getchar()) nm = nm * 10 + c - '0';
	return nm;
}
int n, m, tote, dft, ans, t[M], q[M], r[M], deep[M], top[M], son[M], sz[M], u[M], st[M], id[M], key[M], dfn[M], fa[M];
const int biao = 600;
vector<int> to[M], buc[M << 1];
bool b[M];

void dfs(int now, int f) {
	deep[now] = deep[f] + 1;
	sz[now] = 1;
	for(int i = 0; i < to[now].size(); i++) {
		int vj = to[now][i];
		dfs(vj, now);
		if(sz[son[now]] < sz[vj]) son[now] = vj;
		sz[now] += sz[vj];
	}
}

void dfs(int now) {
	dfn[now] = ++dft;
	if(son[now]) {
		top[son[now]] = top[now];
		dfs(son[now]);
	}
	for(int i = 0; i < to[now].size(); i++) {
		int vj = to[now][i];
		if(vj == son[now]) continue;
		top[vj] = vj;
		dfs(vj);
	}
}

int lca(int a, int b) {
	while(top[a] != top[b]) {
		if(deep[top[a]] < deep[top[b]]) swap(a, b);
		a = fa[top[a]];
	}
	if(deep[a] > deep[b]) swap(a, b);
	return a;
}

bool cmp(int a, int b) {
	return dfn[a] < dfn[b];
}

int rec(int now) {
	int a = b[now];
	for(int i = 0; i < to[now].size(); i++) {
		int vj = to[now][i];
		a += rec(vj);
	}
	r[now] = t[now] - a;
	return a;
}
#define pii pair<int, int>
struct Note {
	int hd, pnt, sum, dx;
	vector<pii> s;
	void clear() {
		hd = pnt = sum = dx = 0;
		vector<pii>().swap(s);
	}
} g[M];

void work(int L, int R) {
	rec(1);
	for(int i = L; i <= R; i++) u[i - L] = q[i];
	sort(u, u + R - L + 1, cmp);
	int tp = 1, num = 1;
	st[1] = key[1] = 1;
	for(int i = 0; i <= R - L; i++) {
		int A = lca(u[i], st[tp]);
		while(deep[A] < deep[st[tp]]) {
			if(deep[st[tp - 1]] <= deep[A]) {
				g[st[tp--]].hd = A;
				if(st[tp] != A) st[++tp] = A, key[++num] = A;
				break;
			}
			g[st[tp]].hd = st[tp - 1];
			tp--;
		}
		if(st[tp] != u[i]) st[++tp] = u[i], key[++num] = u[i];
	}
	for(; tp > 1; tp--) g[st[tp]].hd = st[tp - 1];
	memset(id, 0, sizeof(id));

	for(int i = 1; i <= num; i++) {
		for(int p = fa[key[i]]; p != g[key[i]].hd; p = fa[p]) {
			id[p] = key[i];
		}
	}
	for(int i = 0; i <= (n << 1); i++) vector<int>().swap(buc[i]);

	for(int i = 1; i <= n; i++) if(!b[i]) buc[r[i] + n].push_back(i);
	for(int i = 0; i <= (n << 1); i++) {
		for(int j = 0; j < buc[i].size(); j++) {
			if(id[buc[i][j]]) {
				int o = id[buc[i][j]], ss = g[o].s.size();
				if(ss && g[o].s[ss - 1].first == i - n) g[o].s[ss - 1].second++;
				else g[o].s.push_back(mmp(i - n, 1));
			}
		}
	}
	for(int i = 1; i <= num; i++)
		for(int k = key[i]; g[k].pnt < g[k].s.size() && g[k].s[g[k].pnt].first < 0; g[k].pnt++);
	for(int i = L; i <= R; i++) {
		b[q[i]] ^= 1;
		if(b[q[i]]) {
			if(r[q[i]] < 0) ans--;
			r[q[i]]--;
			for(int p = q[i]; g[p].hd;) {
				g[p].dx--;
				if(g[p].pnt < g[p].s.size() && g[p].s[g[p].pnt].first + g[p].dx < 0) ans += g[p].s[g[p].pnt].second, g[p].pnt++;
				p = g[p].hd, r[p]--;
				if(b[p] == 0 && r[p] == -1) ans++;
			}
		} else {
			r[q[i]]++;
			if(r[q[i]] < 0) ans++;
			for(int p = q[i]; g[p].hd;) {
				g[p].dx++;
				if(g[p].pnt && g[p].s[g[p].pnt - 1].first + g[p].dx >= 0) g[p].pnt--, ans -= g[p].s[g[p].pnt].second;
				p = g[p].hd, r[p]++;
				if(b[p] == 0 && r[p] == 0) ans--;
			}
		}
		cout << ans << ' ';
	}
	for(int i = 1; i <= num; i++) g[key[i]].clear();
}

int main() {
	n = read(), m = read();
	for(int i = 2; i <= n; i++) fa[i] = read(), to[fa[i]].push_back(i);
	dfs(1, 0);
	top[1] = 1;
	dfs(1);
	for(int i = 1; i <= n; i++) t[i] = read();
	for(int i = 1; i <= m; i++) q[i] = read();
	for(int i = 1; i <= m; i += biao) work(i, min(i + biao - 1, m));
	return 0;
}