#include "circuit.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
constexpr int NN = (int)2e5+111;
constexpr int md = (int)1e9+2022;
typedef long long ll;
int a[NN];
std::vector<int> g[NN];
ll dp[2][NN];
ll all[NN];
int p[NN];
int n,m;
void dfs(int v){
if(g[v].empty())
return;
for(auto& to : g[v]){
dfs(to);
}
int sz = g[v].size();
for(int i = 1; i < (1 << sz); i++){
int k = 1;
for(int j = 0; j < sz; j++){
k = (k * dp[i >> j & 1][g[v][j]]) % md;
}
dp[1][v] += __builtin_popcount(i) * k;
dp[1][v] %= md;
}
all[v] = g[v].size();
for(auto& to : g[v]){
all[v] = (all[v] * all[to]) % md;
}
dp[0][v] = (all[v] - dp[1][v] + md) % md;
return;
}
void init(int N, int M, std::vector<int> P, std::vector<int> A) {
p[0] = -1;
for(int i = 1; i < N+M; i++){
g[P[i]].push_back(i);
p[i] = P[i];
}
for(int i = 0; i < M; i++){
a[i+N] = A[i];
dp[1][i+N] = A[i];
dp[0][i+N] = A[i] ^ 1;
all[i+N] = 1;
}
n = N;
m = M;
dfs(0);
return;
}
void go(int v){
if(v == -1)
return;
// cerr << "v = " << v << "\n";
if(g[v].empty()){
go(p[v]);
return;
}
int sz = g[v].size();
dp[1][v] = 0;
dp[0][v] = 0;
for(int i = 1; i < (1 << sz); i++){
int k = 1;
for(int j = 0; j < sz; j++){
k = (k * dp[i >> j & 1][g[v][j]]) % md;
}
dp[1][v] += __builtin_popcount(i) * k % md;
dp[1][v] %= md;
}
all[v] = g[v].size();
for(auto& to : g[v]){
all[v] = (all[v] * all[to]) % md;
}
dp[0][v] = (all[v] - dp[1][v] + md) % md;
go(p[v]);
return;
}
int count_ways(int L, int R) {
for(int i = L; i <= R; i++){
a[i] ^= 1;
dp[1][i] ^= 1;
dp[0][i] ^= 1;
go(p[i]);
}
// dfs(0);
return dp[1][0];
}
/**
3 4 3
-1 0 1 2 1 1 0
1 0 1 0
3 4
4 5
3 6
1 2 1
-1 0 0
0 0
1 1
**/
