#pragma GCC optimize("O3")
#pragma GCC target("avx512vl,avx512dq")
#include "circuit.h"

#include <algorithm>
#include <array>
#include <cassert>
#include <vector>

constexpr int mod = 1e9 + 2022;
int add(int a, int b) {
    return a + b - mod * (a + b >= mod);
}
int mul(int a, int b) {
    return a * 1ULL * b % mod;
}

int n, m;
std::vector<int> prv;
std::vector<int> data;
std::vector<std::vector<int>> nxt;
std::vector<std::array<int, 2>> dp;

void count() {
    for (int i = n - 1; i >= 0; i--) {
        int all = 1, sum = 0;
        for (int id = 0; id < nxt[i].size(); id++) {
            int t = nxt[i][id];
            int s = dp[t][0];

            sum = add(mul(sum, s), mul(all, dp[t][1]));
            all = mul(all, s);
        }

        all = mul(all, nxt[i].size());
        dp[i] = {all, sum};
    }
}

void init(int n, int m, std::vector<int> P, std::vector<int> A) {
    ::n = n;
    ::m = m;
    data = A;
    prv = P;

    dp.resize(n + m);
    for (int i = 0; i < m; i++) {
        dp[n + i] = {1, data[i] == 1};
    }
    nxt.resize(n);
    for (int i = 1; i < n + m; i++) {
        nxt[prv[i]].push_back(i);
    }

    count();
}

int count_ways(int L, int R) {
    L -= n;
    R -= n;
    R++;
    for (int i = L; i < R; i++) {
        data[i] ^= 1;
        dp[n + i] = {1, data[i] == 1};
    }

    count();

    return dp[0][1];
}

In file included from /usr/include/c++/13/vector:63,
                 from circuit.h:1,
                 from answer.code:3:
/usr/include/c++/13/bits/allocator.h: In destructor ‘constexpr std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl()’:
/usr/include/c++/13/bits/allocator.h:184:7: error: inlining failed in call to ‘always_inline’ ‘constexpr std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = int]’: target specific option mismatch
  184 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/13/vector:66:
/usr/include/c++/13/bits/stl_vector.h:133:14: note: called from here
  133 |       struct _Vector_impl
      |              ^~~~~~~~~~~~