#include "circuit.h"
using namespace std;
#include <iostream>
#include <vector>
#include <cassert>
template <std::uint32_t mod>
class modint {
private:
std::uint32_t n;
public:
modint() : n(0) {};
modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {};
static constexpr std::uint32_t get_mod() { return mod; }
std::uint32_t get() const { return n; }
bool operator==(const modint& m) const { return n == m.n; }
bool operator!=(const modint& m) const { return n != m.n; }
modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; }
modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; }
modint operator+(const modint& m) const { return modint(*this) += m; }
modint operator/(const modint& m) const { return modint(*this) * m.inv(); }
modint operator-(const modint& m) const { return modint(*this) -= m; }
modint operator*(const modint& m) const { return modint(*this) *= m; }
modint inv() const { return (*this).pow(mod - 2); }
modint pow(std::uint64_t b) const {
modint ans = 1, m = modint(*this);
while (b) {
if (b & 1) ans *= m;
m *= m;
b >>= 1;
}
return ans;
}
};
using Mint = modint<1'000'002'022>;
int N, M;
vector<int> P;
vector<int> A;
vector<vector<int>> tree;
vector<Mint> weight;
vector<Mint> tot_prod;
struct SQRT {
struct Block {
Mint cur_sum;
Mint tot_sum;
int rev;
int l, r;
void build() {
tot_sum = 0;
cur_sum = 0;
for (int i = l; i <= r; i++) {
A[i] ^= rev;
tot_sum += weight[i]; // can only use once
cur_sum += weight[i] * A[i];
}
rev = 0;
}
void flip() {
rev ^= 1;
cur_sum = tot_sum - cur_sum;
}
};
int BLOCK;
int NBLOCK;
vector<Block> blocks;
SQRT() {;}
SQRT(int _BLOCK) {
BLOCK = _BLOCK;
NBLOCK = (M + BLOCK - 1) / BLOCK;
blocks.resize(NBLOCK);
cerr << NBLOCK << " / " << BLOCK << "\n";
int l = 0, r = 0;
for (int i = 0; i < NBLOCK; i++) {
r = min(M - 1, l + BLOCK - 1);
blocks[i] = Block {0, 0, 0, l, r};
l += BLOCK;
blocks[i].build();
// cerr << blocks[i].l << " - " << blocks[i].r << "\n";
}
}
Mint query(int L, int R) {
int s = L / BLOCK;
int e = R / BLOCK;
Mint ans = 0;
blocks[s].build();
if (e != s)
blocks[e].build();
for (int i = L; i <= min(blocks[s].r, R); i++) {
blocks[s].cur_sum -= weight[i] * A[i];
A[i] ^= 1;
blocks[s].cur_sum += weight[i] * A[i];
// cerr << i << " " << A[i] << "\n";
}
for (int i = s + 1; i <= e - 1; i++) {
blocks[i].flip();
}
if (e > s) {
for (int i = blocks[e].l; i <= R; i++) {
blocks[e].cur_sum -= weight[i] * A[i];
A[i] ^= 1;
blocks[e].cur_sum += weight[i] * A[i];
}
}
for (auto & b : blocks)
ans += b.cur_sum;
return ans;
}
};
SQRT ds;
Mint dfs1(int v) {
if (v >= N) {
return tot_prod[v] = 1;
}
Mint & res = tot_prod[v];
res = size(tree[v]);
for (auto u : tree[v]) {
res *= dfs1(u);
}
return res;
}
void dfs2(int v, Mint w) {
if (v >= N) {
weight[v - N] = w;
return;
}
int n = size(tree[v]);
assert(n);
vector<Mint> suf(n);
suf[n-1] = tot_prod[tree[v].back()];
for (int i = n - 2; i >= 0; i--) {
suf[i] = tot_prod[tree[v][i]] * suf[i+1];
}
Mint pref = 1;
for (int i = 0; i < n; i++) {
Mint level = (i + 1 < n ? suf[i+1]: 1);
level *= pref;
dfs2(tree[v][i], w * level);
pref *= tot_prod[tree[v][i]];
}
}
void init(int N, int M, std::vector<int> P, std::vector<int> A) {
::N = N;
::M = M;
::P = P;
::A = A;
tree.resize(N);
for (int i = 1; i < N + M; i++) {
tree[P[i]].push_back(i);
}
tot_prod.resize(N + M);
dfs1(0);
weight.resize(M);
dfs2(0, 1);
ds = SQRT(400);
}
int count_ways(int L, int R) {
// naive
// cerr << "count: " << L << " " << R << "\n";
L -= N;
R -= N;
// for (int i = L; i <= R; i++) {
// A[i] ^= 1;
// }
// Mint res = 0;
// for (int i = 0; i < M; i++)
// res += weight[i] * Mint(A[i]);
// return res.get();
return ds.query(L, R).get();
}
