#include "circuit.h"
#include <bits/stdc++.h>
using namespace std;
const long long modulo = 1e9+2022;
struct segtree {
vector<pair<long long,long long>> tree;
int N;
vector<bool> lazy;
segtree(){}
void build(int x,int L,int R,vector<long long> &arr,vector<int> &A) {
if(L==R) {
if(A[L-1]) tree[x].first=arr[L-1];
else tree[x].second=arr[L-1];
return;
}
int mid = (L+R)/2;
build(2*x,L,mid,arr,A);
build(2*x+1,mid+1,R,arr,A);
tree[x].first=(tree[2*x].first+tree[2*x+1].first)%modulo;
tree[x].second=(tree[2*x].second+tree[2*x+1].second)%modulo;
}
segtree(int N,vector<long long> &arr,vector<int> &A):tree(4*N),N(N),lazy(4*N) {
build(1,1,N,arr,A);
}
void update(int x,int L,int R,int qL,int qR) {
if(lazy[x]) {
swap(tree[x].first,tree[x].second);
lazy[x]=false;
if(L!=R) {
lazy[2*x]=!lazy[2*x];
lazy[2*x+1]=!lazy[2*x+1];
}
}
if(qR<L or R<qL)return;
if(qL<=L and R<=qR) {
swap(tree[x].first,tree[x].second);
if(L!=R) {
lazy[2*x]=!lazy[2*x];
lazy[2*x+1]=!lazy[2*x+1];
}
return;
}
int mid = (L+R)/2;
update(2*x,L,mid,qL,qR);
update(2*x+1,mid+1,R,qL,qR);
tree[x].first=(tree[2*x].first+tree[2*x+1].first)%modulo;
tree[x].second=(tree[2*x].second+tree[2*x+1].second)%modulo;
}
void update(int L,int R) {
update(1,1,N,L+1,R+1);
}
long long get() {
return tree[1].first;
}
};
namespace {
int N,M;
vector<int> A;
vector<long long> arr;
segtree seg;
}
void init(int N,int M,vector<int> P,vector<int> A){
::N = N;
::M = M;
::A = A;
arr = vector<long long>(M);
vector<vector<int>> adj(N);
vector<vector<pair<long long,long long>>> ways(N);
for(int i=1;i<N+M;i++){adj[P[i]].emplace_back(i);ways[P[i]].emplace_back(1,1);}
{
function<long long(int)> dfs = [&](int x){
if(x>=N)return 1ll;
long long tot_ways = adj[x].size();
for(int i=0;i<adj[x].size();i++) {
ways[x][i].first=ways[x][i].second=dfs(adj[x][i]);
tot_ways=(tot_ways*ways[x][i].first)%modulo;
if(i)ways[x][i].first=(ways[x][i].first*ways[x][i-1].first)%modulo;
}
for(int i=adj[x].size()-2;i>=0;i--)ways[x][i].second=(ways[x][i].second*ways[x][i+1].second)%modulo;
return tot_ways;
};
dfs(0);
}
{
function<void(int,long long)> dfs = [&](int x,long long offset) {
if(x>=N) {
arr[x-N]=offset;
return;
}
for(int i=0;i<adj[x].size();i++) {
long long tot = offset;
if(i)tot=(tot*ways[x][i-1].first)%modulo;
if(i!=adj[x].size()-1)tot=(tot*ways[x][i+1].second)%modulo;
dfs(adj[x][i],tot);
}
};
dfs(0,1);
}
seg = segtree(M,arr,A);
}
int count_ways(int L,int R){
L-=N;R-=N;
seg.update(L,R);
return seg.get();
}
