#include <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef long long ll;
typedef pair<int,int> ii;
#define ALL(x) x.begin(),x.end()
#define SIZE(x) (int)x.size()
#define forsn(i,s,n) for(int i=int(s);i<int(n);i++)
#define forn(i,n) for(int i=0;i<int(n);i++)
#define dforsn(i,s,n) for(int i=int(n)-1;i>=int(s);i--)
#define dforn(i,n) for(int i=int(n)-1;i>=0;i--)
#define fst first
#define snd second
#define pb push_back
const int MAXN = 2e5;
const int MOD = 1e9+2022;
vi s, adj[MAXN];
int n, m;
int dp[MAXN][2];
int mul(int x, int y) {
return int(1LL*x*y%MOD);
}
void add(int &x, int y) {
x+=y;
if(x>=MOD) x-=MOD;
}
void compute_dp(int u) {
int l=2*u+1, r=2*u+2;
int aux = mul(dp[l][0], dp[r][1]);
add(aux, mul(dp[l][1], dp[r][0]));
dp[u][1] = dp[u][0] = aux;
aux = mul(mul(2, dp[l][0]), dp[r][0]);
add(dp[u][0], aux);
aux = mul(mul(2, dp[l][1]), dp[r][1]);
add(dp[u][1], aux);
}
void dfs_st(int u) {
if(u>=n) {
dp[u][s[u-n]] = 1;
dp[u][!s[u-n]] = 0;
return;
}
dfs_st(2*u+1), dfs_st(2*u+2);
compute_dp(u);
}
bool bt=true;
void init(int N, int M, vi P, vi A) {
bt &= M==N+1;
bt &= !(M&(M-1));
s=A, n=N, m=M;
forsn(i,1,n+m) {
adj[P[i]].pb(i);
bt &= P[i]==(i-1)/2;
}
if(bt) dfs_st(0);
}
bool lazy[MAXN];
void pass(int u) {
if(!lazy[u]) return;
if(2*u+2<MAXN) {
lazy[2*u+1] ^= 1;
lazy[2*u+2] ^= 1;
}
swap(dp[u][0], dp[u][1]);
lazy[u] = false;
}
void update(int ql, int qr, int nl, int nr, int u) {
pass(u);
if(qr <= nl || nr <= ql) {
return;
}
if(ql <= nl && nr <= qr) {
lazy[u] ^= 1;
pass(u);
return;
}
int nm=(nl+nr)/2;
update(ql,qr,nl,nm,2*u+1);
update(ql,qr,nm,nr,2*u+2);
compute_dp(u);
}
ii dfs(int u) {
int c=SIZE(adj[u]);
if(!c) return {!s[u-n], s[u-n]};
vi ways(c+1,0);
ways[0] = 1;
forn(i,c) {
ii child=dfs(adj[u][i]);
dforn(j,c+1) {
ways[j] = mul(ways[j],child.fst);
if(j) add(ways[j],mul(ways[j-1],child.snd));
}
}
ii ans = {0,0};
forsn(i,1,c+1) {
forn(j,i) add(ans.fst, ways[j]);
forsn(j,i,c+1) add(ans.snd, ways[j]);
}
return ans;
}
int count_ways(int L, int R) {
if(bt) {
update(L-n, R-n+1, 0, m, 0);
return dp[0][1];
}
forsn(i,L,R+1) s[i-n]^=1;
return int(dfs(0).snd);
}
