#include "circuit.h"
#include <bits/stdc++.h>
using namespace std;
#define int ll
using ll = long long;
using pii = pair<int,int>;
const int nmax = 1e5 + 5, mod = 1e9 + 2022;
int n, m;
int cost[nmax];
namespace AINT {
int aint[nmax * 4], inv[nmax * 4], lazy[nmax * 4];
int init(int node = 1, int cl = 0, int cr = m - 1) {
lazy[node] = 0;
inv[node] = 0;
if(cl == cr) {
aint[node] = cost[cl];
return aint[node];
}
int mid = cl + cr >> 1;
return aint[node] = (init(2 * node, cl, mid) + init(2 * node + 1, mid + 1, cr)) % mod;
}
void push(int node, bool to) {
if(lazy[node])
swap(aint[node], inv[node]);
if(to)
lazy[node * 2] ^= lazy[node],
lazy[node * 2 + 1] ^= lazy[node];
lazy[node] = 0;
return;
}
int upd(int l, int r, int node = 1, int cl = 0, int cr = m - 1) {
push(node, cl != cr);
if(r < cl || cr < l)
return aint[node];
if(l <= cl && cr <= r) {
lazy[node] = 1;
push(node, cl != cr);
//cerr << l << " <= " << cl << ' ' << cr << " <= " << r << '\n';
//cerr << aint[node] << ' ' << inv[node] << "\n\n";
return aint[node];
}
int mid = cl + cr >> 1;
aint[node] = ((ll)upd(l, r, 2 * node, cl, mid) + upd(l, r, 2 * node + 1, mid + 1, cr)) % mod;
inv[node] = ((ll)inv[2 * node] + inv[2 * node + 1]) % mod;
return aint[node];
}
}
vector<int> g[nmax * 2];
int prod[nmax * 2];
void initdfs(int node) {
prod[node] = max(1LL, (int)g[node].size());
for(auto x : g[node])
initdfs(x),
prod[node] = ((ll)prod[node] * prod[x]) % mod;
return;
}
void initcost(int node, int accum = 1) {
if(g[node].size() == 0) {
cost[node - n] = accum;
return;
}
vector<int> pref(g[node].size()), suff(g[node].size());
int tmp = 1;
for(int i = 0; i < g[node].size(); i++) {
pref[i] = tmp;
tmp = (ll)tmp * prod[g[node][i]] % mod;
}
tmp = 1;
for(int i = g[node].size() - 1; i >= 0; i--) {
suff[i] = tmp;
tmp = (ll)tmp * prod[g[node][i]] % mod;
}
for(int i = 0; i < g[node].size(); i++) {
initcost(g[node][i], (ll)accum * pref[i] % mod * suff[i] % mod);
}
return;
}
#undef int
void init(int N, int M, std::vector<int> P, std::vector<int> A) {
#define int ll
for(int i = 1; i < N + M; i++) {
g[P[i]].push_back(i);
}
tie(n, m) = pii{N, M};
initdfs(0);
initcost(0, 1);
AINT::init();
for(int i = 0; i < m; i++) {
//cerr << cost[i] << ' ';
if(A[i] == 0)
AINT::upd(i, i);
//cerr << A[i] << ' ' << AINT::aint[1] << '\n';
}
//cerr << '\n';
return;
}
#undef int
int count_ways(int L, int R) {
return AINT::upd(L - n, R - n);
}
