#include "circuit.h"
#include <bits/stdc++.h>
using namespace std;
constexpr int mod = 1000002022;
int N, M;
vector<int> P, A, st, lazy, len;
vector<vector<int>> ch;
int add(int a, int b) {
int c = a + b;
if (c >= mod) {
c -= mod;
}
return c;
}
int mul(int a, int b) {
return 1LL * a * b % mod;
}
int sub(int a, int b) {
int c = a - b;
if (c < 0) {
c += mod;
}
return c;
}
int cont;
bool bintree;
void apply(int p, int z) {
if (z == 0) {
return;
}
st[p] = len[p] - st[p];
lazy[p] ^= 1;
}
void pull(int p) {
st[p] = st[p * 2] + st[p * 2 + 1];
}
void push(int p) {
apply(p * 2, lazy[p]);
apply(p * 2 + 1, lazy[p]);
lazy[p] = 0;
}
void update(int p, int l, int r, int L, int R) {
if (R <= l || r <= L) {
return;
}
if (L <= l && r <= R) {
apply(p, 1);
return;
}
int m = (l + r) / 2;
push(p);
update(p * 2, l, m, L, R);
update(p * 2 + 1, m, r, L, R);
pull(p);
}
void init(int n, int m, vector<int> p, vector<int> a) {
N = n, M = m;
P = p, A = a;
ch.resize(N);
for (int i = 1; i < N + M; i++) {
ch[P[i]].push_back(i);
}
bintree = 0;
if (N + 1 == M && __builtin_popcount(M) == 1) {
bintree = 1;
for (int i = 1; i < N + M; i++) {
if (P[i] != (i - 1) / 2) {
bintree = 0;
}
}
if (bintree) {
int lg = __lg(M);
cont = 1;
int s = 1;
for (int i = 0; i < lg; i++) {
cont = mul(cont, s);
s = mul(2, mul(s, s));
}
st.resize(2 * M);
len.resize(2 * M);
lazy.resize(2 * M);
for (int i = 0; i < M; i++) {
st[i + M] = A[i];
len[i + M] = 1;
}
for (int i = M - 1; i; i--) {
st[i] = st[i * 2] + st[i * 2 + 1];
len[i] = len[i * 2] + len[i * 2 + 1];
}
}
}
}
int count_ways(int L, int R) {
if (bintree) {
update(1, 0, M, L - N, R - N + 1);
return mul(st[1], cont);
}
for (int i = L; i <= R; i++) {
A[i - N] ^= 1;
}
vector<int> tot(N + M), on(N + M), off(N + M);
for (int i = N + M - 1; i >= 0; i--) {
if (i >= N) {
tot[i] = 1;
if (A[i - N] == 0) {
off[i] = 1;
} else {
on[i] = 1;
}
} else {
int x = ch[i][0];
int y = ch[i][1];
tot[i] = mul(2, mul(tot[x], tot[y]));
on[i] = add(mul(tot[x], on[y]), mul(tot[y], on[x]));
off[i] = sub(tot[i], on[i]);
}
}
return on[0];
}
