#include "circuit.h"
#include <bits/stdc++.h>
#define endl "\n"
using namespace std;
const long long mod = 1e9 + 2022;
const int MAXN = 1e5+5;
int n,m;
int p[MAXN],a[MAXN];
vector<int>g[MAXN];
long long dp[MAXN][2];
long long pd[MAXN];
void dfs(int beg)
{
if(beg >= n) return;
for(int nb : g[beg]) dfs(nb);///smetnati
int sz = g[beg].size();
for(int i = 0; i <= sz; i++) pd[i] = 0;
pd[0] = 1;
/*cout << "in_dfs " << beg << endl;
bool f = false;
if(beg == 1) f = true;
if(f) cout << "special pechat" << endl;
for(int i = 0; i <= sz; i++) cout << pd[i] << " ";
cout << endl;*/
for(int j = 0; j < sz; j++)
{
int nb = g[beg][j];
for(int i = sz; i >= 0; i--)
{
pd[i] = (pd[i]*dp[nb][0])%mod;
pd[i] += (pd[i-1]*dp[nb][1])%mod;
pd[i] %= mod;
}
/*cout << nb << " " << dp[nb][0] << " " << dp[nb][1] << "-> ";
for(int i = 0; i <= sz; i++) cout << pd[i] << " ";
cout << endl;*/
}
//for(int i = 0; i <= sz; i++) cout << pd[i] << " ";
//cout << endl;
for(int br1 = 0; br1 <= sz; br1++)
{
dp[beg][1] += (pd[br1]*(br1))%mod;
dp[beg][1] %= mod;
dp[beg][0] += (pd[br1]*(sz-br1))%mod;
dp[beg][0] %= mod;
}
}
void dfs_but(int beg)
{
while(true)
{
beg = p[beg];
if(beg == -1) break;
int sz = g[beg].size();
for(int i = 0; i <= sz; i++) pd[i] = 0;
pd[0] = 1;
/*cout << "in_dfs " << beg << endl;
bool f = false;
if(beg == 1) f = true;
if(f) cout << "special pechat" << endl;
for(int i = 0; i <= sz; i++) cout << pd[i] << " ";
cout << endl;*/
for(int j = 0; j < sz; j++)
{
int nb = g[beg][j];
for(int i = sz; i >= 0; i--)
{
pd[i] = (pd[i]*dp[nb][0])%mod;
pd[i] += (pd[i-1]*dp[nb][1])%mod;
pd[i] %= mod;
}
/*cout << nb << " " << dp[nb][0] << " " << dp[nb][1] << "-> ";
for(int i = 0; i <= sz; i++) cout << pd[i] << " ";
cout << endl;*/
}
//for(int i = 0; i <= sz; i++) cout << pd[i] << " ";
//cout << endl;
dp[beg][0] = dp[beg][1] = 0;
for(int br1 = 0; br1 <= sz; br1++)
{
dp[beg][1] += (pd[br1]*(br1))%mod;
dp[beg][1] %= mod;
dp[beg][0] += (pd[br1]*(sz-br1))%mod;
dp[beg][0] %= mod;
}
}
}
void solve()
{
/*cout << endl;
cout << "START solve" << endl;
for(int i = n; i < n+m; i++) cout << a[i-n] << " ";
cout << endl;*/
for(int i = 0; i < n+m; i++) dp[i][0] = dp[i][1] = 0;
for(int i = 0; i < m; i++) dp[i+n][a[i]] = 1;
dfs(0);
/*for(int i = 0; i < n+m; i++) cout << dp[i][0] << " ";
cout << endl;
for(int i = 0; i < n+m; i++) cout << dp[i][1] << " ";
cout << endl;*/
}
void init(int N, int M, vector<int> P, vector<int> A)
{
n = N;
m = M;
for(int i = 0; i < n+m; i++)
{
p[i] = P[i];
if(i) g[p[i]].push_back(i);
}
for(int i = 0; i < m; i++) a[i] = A[i];
solve();
}
int count_ways(int L, int R)
{
L -= n;
R -= n;
for(int i = L; i <= R; i++)
{
a[i] ^= 1;
swap(dp[i+n][0],dp[i+n][1]);
}
int ver = R + n;
dfs_but(ver);
return (int)dp[0][1];
}
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