#include "circuit.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr int mod = 1000002022;
int add(int x, int y) {
int z = x + y;
if (z >= mod) {
z -= mod;
}
return z;
}
int sub(int x, int y) {
int z = x - y;
if (z < 0) {
z += mod;
}
return z;
}
int mul(int x, int y) {
return (ll)x * y % mod;
}
int N, M;
vector<int> P, A, tot, dp, lazy;
void apply(int p, int v) {
if (v) {
dp[p] = sub(tot[p], dp[p]);
}
lazy[p] ^= v;
}
void push(int p) {
apply(p * 2 + 1, lazy[p]);
apply(p * 2 + 2, lazy[p]);
lazy[p] = 0;
}
void pull(int p) {
dp[p] = add(mul(dp[p * 2 + 1], tot[p * 2 + 2]), mul(dp[p * 2 + 2], tot[p * 2 + 1]));
}
int T;
void init(int n, int m, vector<int> p, vector<int> a) {
N = n, M = m;
P = p, A = a;
if (M == N + 1 && (1 << __lg(M)) == M) {
tot.resize(N + M);
dp.resize(N + M);
lazy.resize(N + M);
for (int i = 0; i < M; i++) {
dp[i + N] = A[i];
tot[i + N] = 1;
}
for (int i = N - 1; i >= 0; i--) {
int x = i * 2 + 1;
int y = i * 2 + 2;
pull(i);
tot[i] = mul(2, mul(tot[x], tot[y]));
}
T = 1;
int x = N;
while (x > 0) {
T = mul(T, tot[x]);
x = (x - 1) / 2;
}
}
}
void update(int p, int l, int r, int L, int R) {
if (R <= l || r <= L) {
return;
}
if (L <= l && r <= R) {
apply(p, 1);
return;
}
int m = (l + r + 1) / 2;
push(p);
update(p * 2 + 1, l, m, L, R);
update(p * 2 + 2, m, r, L, R);
pull(p);
}
int count_ways(int L, int R) {
if (N <= 1000 && M <= 1000) {
vector dp(N, vector{1});
vector<int> on(N + M), off(N + M), tot(N + M, 1);
for (int i = L; i <= R; i++) {
A[i - N] ^= 1;
}
for (int i = N + M - 1; i >= 0; i--) {
if (i >= N) {
on[i] = A[i - N];
off[i] = tot[i] - on[i];
} else {
int sum = 0;
for (int j = dp[i].size() - 1; j; j--) {
sum = add(sum, dp[i][j]);
on[i] = add(on[i], sum);
}
tot[i] = mul(tot[i], (int)dp[i].size() - 1);
off[i] = sub(tot[i], on[i]);
}
if (i) {
int K = dp[P[i]].size();
dp[P[i]].resize(K + 1);
for (int j = K; j; j--) {
dp[P[i]][j] = add(mul(dp[P[i]][j], off[i]), mul(dp[P[i]][j - 1], on[i]));
}
dp[P[i]][0] = mul(dp[P[i]][0], off[i]);
tot[P[i]] = mul(tot[P[i]], tot[i]);
}
}
return on[0];
}
if (A[L - N] == 0) {
dp[0] = add(dp[0], T);
} else {
dp[0] = sub(dp[0], T);
}
A[L - N] ^= 1;
return dp[0];
// update(0, 0, M, L - N, R - N + 1);
// return dp[0];
}
