#include "circuit.h"
#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define fi first
#define se second
#define lf ((id<<1))
#define rg ((id<<1)|1)
#define md ((l+r)>>1)
using namespace std;
const int MAXN = 3e5+10;
const ll MOD = 1e9+2022;
ll sum(ll a, ll b){ return (a+b)%MOD;}
ll sub(ll a, ll b){ return (a+MOD-b)%MOD;}
void chsum(ll &a, ll b){ a = (a+b)%MOD;}
ll mul(ll a, ll b){ return (a*b)%MOD; }
void chmul(ll &a, ll b){ a = (a*b)%MOD;}
void chmn(auto &a, auto b){ a = min(a, b); }
void chmx(auto &a, auto b){ a = max(a, b); }
int n, m, par[MAXN], a[MAXN];
ll dp[MAXN][3], on[MAXN], val[MAXN];
vector<int> adj[MAXN];
void dfs(int nw){
if(adj[nw].empty()){
dp[nw][0] = dp[nw][1] = 0;
dp[nw][a[nw]] = 1;
return;
}
for(auto nx : adj[nw]) dfs(nx);
int siz = adj[nw].size();
for(int i=0; i<=siz+1; i++) on[i] = 0;
on[0] = 1;
for(auto nx : adj[nw]){
for(int i=siz; i>=0; i--){
on[i] = mul(on[i], dp[nx][0]);
if(i>=1)
chsum(on[i], mul(on[i-1], dp[nx][1]) );
}
}
for(int i=siz; i>=0; i--) chsum(on[i], on[i+1]); // suffix
dp[nw][1] = dp[nw][0] = 0;
for(int i=1; i<=siz; i++) chsum(dp[nw][1], on[i]); //i...siz
for(int i=1; i<=siz; i++) chsum(dp[nw][0], sub(on[0], on[i])); //0..i-1
}
struct node {
ll zer = 0, one = 0;
} NOL;
struct seg {
node st[4*MAXN]; int laz[4*MAXN];
node mrg(node a, node b){
node ret;
ret.one = sum(a.one, b.one);
ret.zer = sum(a.zer, b.zer);
return ret;
}
void push(int id, int v){
swap(st[id].one, st[id].zer);
laz[id] ^= v;
}
void bnc(int id){
if(laz[id]==0) return;
push(lf,laz[id]); push(rg,laz[id]);
laz[id] = 0;
}
void bd(int id, int l, int r){
if(l==r){
if(a[l+n] == 1){
st[id].one = val[l+n];
} else {
st[id].zer = val[l+n];
}
return;
}
bd(lf,l,md); bd(rg,md+1,r);
st[id] = mrg(st[lf], st[rg]);
}
node upd(int id, int l, int r, int x, int y){
if(x<=l && r<=y){
push(id, 1);
return st[id];
}
if(r<x || y<l) return st[id];
bnc(id);
return st[id] = mrg(upd(lf,l,md,x,y), upd(rg,md+1,r,x,y));
}
} A;
void init(int N, int M, std::vector<int> P, std::vector<int> AA) {
n = N; m = M;
for(int i=1; i<=n+m; i++){
par[i] = P[i-1]+1;
adj[par[i]].pb(i);
}
for(int i=1; i<=m; i++){
a[i+n] = 1;
dfs(1);
val[i+n] = dp[1][1];
// cout << i << ' ' << val[i+n] << " pp\n";
a[i+n] = 0;
}
for(int i=1; i<=m; i++){
a[i+n] = AA[i-1];
}
A.bd(1,1,m);
}
int count_ways(int L, int R) {
int l = L+1, r = R+1;
// for(int i=l; i<=r; i++) a[i] = 1-a[i];
A.upd(1,1,m,l-n,r-n);
// for(int i=1; i<=13; i++){
// cout << i << ' ' <<dp[i][0] << ' ' << dp[i][1] << " xx\n";
// }
return (int)A.st[1].one;
}
