#include "circuit.h"
#include <cmath>
#include <algorithm>
#include <vector>
#include <iostream>
using namespace std;
typedef long long ll;
int NN, MM;
const ll N = 2e5 + 10, mod = 1000002022;
int p[N], d[N];
int lazy[4 * N];
int a[N], cnt[N];
ll pref[N];
bool ch = true, ch2 = true;
pair <ll, ll> tree[4 * N];
ll tree2[4 * N];
ll binpow(ll a, ll n) {
if (n == 0) return 1LL;
if (n % 2 == 0) {
ll u = binpow(a, n / 2);
return (u * u) % mod;
}
return (a * binpow(a, n - 1)) % mod;
}
void pushh(int v, int tl, int tr) {
if (lazy[v]) {
lazy[v] = 0;
if (tl != tr) {
lazy[2 * v] = (lazy[2 * v] + 1) % 2;
lazy[2 * v + 1] = (lazy[2 * v + 1] + 1) % 2;
swap(tree[2 * v].first, tree[2 * v].second);
swap(tree[2 * v + 1].first, tree[2 * v + 1].second);
}
}
}
void build_tree(int v, int tl, int tr) {
if (tl == tr) {
if (a[tl] == 1) tree[v] = { 1, 0 };
else tree[v] = { 0, 1 };
}
else {
int tm = (tl + tr) / 2;
build_tree(2 * v, tl, tm);
build_tree(2 * v + 1, tm + 1, tr);
ll a = tree[2 * v].first, b = tree[2 * v].second, c = tree[2 * v + 1].first, d = tree[2 * v + 1].second;
tree[v].first = 2 * a * c + a * d + b * c;
tree[v].second = 2 * b * d + a * d + b * c;
tree[v].first %= mod;
tree[v].second %= mod;
}
}
void update(int v, int tl, int tr, int l, int r) {
if (tl > r || tr < l) return;
if (tl >= l && tr <= r) {
lazy[v] = (lazy[v] + 1) % 2;
swap(tree[v].first, tree[v].second);
return;
}
pushh(v, tl, tr);
int tm = (tl + tr) / 2;
update(2 * v, tl, tm, l, r);
update(2 * v + 1, tm + 1, tr, l, r);
ll a = tree[2 * v].first, b = tree[2 * v].second, c = tree[2 * v + 1].first, d = tree[2 * v + 1].second;
tree[v].first = 2 * a * c + a * d + b * c;
tree[v].second = 2 * b * d + a * d + b * c;
tree[v].first %= mod;
tree[v].second %= mod;
}
void build_tree2(int v, int tl, int tr) {
if (tl == tr) {
if (a[tl]) {
tree2[v] = pref[tl];
if (tl) tree2[v] -= pref[tl - 1];
tree2[v] = (tree2[v] + mod) % mod;
}
else tree2[v] = 0;
}
else {
int tm = (tl + tr) / 2;
build_tree2(2 * v, tl, tm);
build_tree2(2 * v + 1, tm + 1, tr);
tree2[v] = tree2[2 * v] + tree2[2 * v + 1];
tree2[v] %= mod;
}
}
void pushh2(int v, int tl, int tr) {
if (lazy[v]) {
lazy[v] = 0;
if (tl != tr) {
lazy[2 * v] = (lazy[2 * v] + 1) % 2;
lazy[2 * v + 1] = (lazy[2 * v + 1] + 1) % 2;
int tm = (tl + tr) / 2;
ll u = pref[tm];
if (tl) u -= pref[tl - 1];
u += mod;
u %= mod;
tree2[2 * v] = (u + mod - tree2[2 * v]) % mod;
u = pref[tr] - pref[tm] + mod;
u %= mod;
tree2[2 * v + 1] = (u + mod - tree2[2 * v + 1]) % mod;
}
}
}
void update2(int v, int tl, int tr, int l, int r) {
if (tl > r || tr < l) return;
if (tl >= l && tr <= r) {
lazy[v] = (lazy[v] + 1) % 2;
ll u = pref[tr];
if (tl) u -= pref[tl - 1];
u += mod;
u %= mod;
tree2[v] = (u - tree2[v] + mod) % mod;
return;
}
pushh2(v, tl, tr);
int tm = (tl + tr) / 2;
update2(2 * v, tl, tm, l, r);
update2(2 * v + 1, tm + 1, tr, l, r);
tree2[v] = tree2[2 * v] + tree2[2 * v + 1];
tree2[v] %= mod;
}
pair<ll, ll> dp[N];
vector <vector<int>> G;
void dfs(int v, int p) {
vector <int> childrens;
for (auto it : G[v]) {
if (it == p) continue;
dfs(it, v);
childrens.push_back(it);
}
if (childrens.empty()) {
dp[v].first = 1;
dp[v].second = 0;
if (a[v - NN] == 0) swap(dp[v].first, dp[v].second);
return;
}
vector <vector<ll>> w((int)childrens.size());
for (int i = 0; i < (int)w.size(); i++) {
w[i].resize(i + 2);
}
w[0][0] = dp[childrens[0]].second;
w[0][1] = dp[childrens[0]].first;
for (int i = 1; i < (int)childrens.size(); i++) {
for (int j = 0; j <= i + 1; j++) {
w[i][j] = 0;
if (j != i + 1) w[i][j] += w[i - 1][j] * dp[childrens[i]].second;
if (j > 0) w[i][j] += w[i - 1][j - 1] * dp[childrens[i]].first;
w[i][j] %= mod;
}
}
ll ff = 0, ss = 0;
for (int j = 0; j <= (int)childrens.size(); j++) {
ll u = w[(int)childrens.size() - 1][j] * (ll(j));
u %= mod;
ff += u;
ff %= mod;
u = w[(int)childrens.size() - 1][j] * ((ll)childrens.size() - ll(j));
u %= mod;
ss += u;
ss %= mod;
}
dp[v].first = ff;
dp[v].second = ss;
}
void init(int N, int M, std::vector<int> P, std::vector<int> A) {
NN = N, MM = M;
for (int i = 0; i < N + M; i++) {
p[i] = P[i];
if (i == 0) d[0] = 0;
if (i > 0 && p[i] != (i - 1) / 2) ch = false;
if (i) {
d[i] = d[P[i]] + 1;
cnt[P[i]]++;
}
}
for (int i = 0; i < N; i++) {
if (cnt[i] != 2) ch2 = false;
}
for (int i = 0; i < M; i++) {
a[i] = A[i];
}
if (M != N + 1) ch = false;
int u = log2(M);
if ((1 << u) != M) ch = false;
if (ch) build_tree(1, 0, M - 1);
else if (ch2) {
for (int i = 0; i < M; i++) {
pref[i] = binpow(2, N - d[i + N]);
if (i) pref[i] += pref[i - 1];
pref[i] %= mod;
}
build_tree2(1, 0, MM - 1);
}
else {
G.resize(N + M);
for (int i = 1; i < N + M; i++) {
G[p[i]].push_back(i);
}
dfs(0, -1);
}
}
int count_ways(int L, int R) {
if (ch) {
update(1, 0, MM - 1, L - NN, R - NN);
return tree[1].first;
}
else if (ch2) {
update2(1, 0, MM - 1, L - NN, R - NN);
return tree2[1];
}
else {
for (int i = L - NN; i <= R - NN; i++) {
a[i] = (a[i] + 1) % 2;
}
dfs(0, -1);
return dp[0].first;
}
}
