This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
const int L = 20;
int S[1 << L], A[1 << L], B[1 << L], popcnt[1 << L];
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
for (int i = 1; i < 1 << L; ++i) {
popcnt[i] = popcnt[i - (i & -i)] + 1;
}
int l, q;
string s;
cin >> l >> q >> s;
for (int i = 0; i < 1 << l; ++i) {
S[i] = A[i] = B[((1 << l) - 1) ^ i] = s[i] - '0';
}
for (int i = 0; i < l; ++i) {
for (int mask = 0; mask < 1 << l; ++mask) {
if (mask & 1 << i) {
A[mask] += A[mask ^ 1 << i];
}
}
}
for (int i = 0; i < l; ++i) {
for (int mask = 0; mask < 1 << l; ++mask) {
if (mask & 1 << i) {
B[mask] += B[mask ^ 1 << i];
}
}
}
while (q--) {
string t;
cin >> t;
reverse(t.begin(), t.end());
int mask0 = 0, mask1 = 0, mask2 = 0;
for (int i = 0; i < l; ++i) {
if (t[i] == '0') {
mask0 ^= 1 << i;
} else if (t[i] == '1') {
mask1 ^= 1 << i;
} else {
mask2 ^= 1 << i;
}
}
int ans = 0;
if (popcnt[mask1] <= 6) {
for (int mask = mask1; mask; mask = (mask - 1) & mask1) {
ans += A[mask ^ mask2] * (popcnt[mask ^ mask1] & 1 ? -1 : 1);
}
ans += A[mask2] * (popcnt[mask1] & 1 ? -1 : 1);
} else if (popcnt[mask0] <= 6) {
for (int mask = mask0; mask; mask = (mask - 1) & mask0) {
ans += B[mask ^ mask2] * (popcnt[mask ^ mask0] & 1 ? -1 : 1);
}
ans += B[mask2] * (popcnt[mask0] & 1 ? -1 : 1);
} else {
for (int mask = mask2; mask; mask = (mask - 1) & mask2) {
ans += S[mask ^ mask1];
}
ans += S[mask1];
}
cout << ans << '\n';
}
return 0;
}
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