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>
#define ll long long
using namespace std;
ll n, q, f[(1 << 20)], g[(1 << 20)], a[(1 << 20)];
int main() {
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
cin >> n >> q;
for (int i = 0; i < (1 << n); i++) {
char c; cin >> c;
a[i] = c - '0';
f[i] = g[i] = c - '0';
}
for (int i = 0; i < n; i++)
for (int j = 0; j < (1 << n); j++)
if (j >> i & 1)
f[j] += f[j ^ (1 << i)];
for (int i = 0; i < n; i++)
for (int j = 0; j < (1 << n); j++)
if (!(j >> i & 1))
g[j] += g[j ^ (1 << i)];
while (q--) {
string s; cin >> s;
reverse(s.begin(), s.end());
vector < int > v0, v1, v2;
int msk1 = 0, msk2 = 0;
for (int i = 0; i < n; i++) {
if (s[i] == '0') v0.push_back(i);
if (s[i] == '1') {
v1.push_back(i);
msk1 ^= (1 << i);
}
if (s[i] == '?') {
v2.push_back(i);
msk2 ^= (1 << i);
}
}
int len = min(v0.size(), min(v1.size(), v2.size()));
if (len == (int)v0.size()) {
ll res = 0;
for (int j = 0; j < (1 << (int)v0.size()); j++) {
int newmsk = msk1;
for (int i = 0; i < (int)v0.size(); i++) if (j >> i & 1) newmsk ^= (1 << v0[i]);
if (__builtin_popcount(j) & 1) res -= g[newmsk];
else res += g[newmsk];
}
cout << res << '\n';
continue;
}
if (len == (int)v1.size()) {
ll res = 0;
for (int j = 0; j < (1 << (int)v1.size()); j++) {
int newmsk = msk2;
for (int i = 0; i < (int)v1.size(); i++) if (j >> i & 1) newmsk ^= (1 << v1[i]);
if ((__builtin_popcount(j) + v1.size()) & 1) res -= f[newmsk];
else res += f[newmsk];
}
cout << res << '\n';
continue;
}
if (len == (int)v2.size()) {
ll res = 0;
for (int j = 0; j < (1 << (int)v2.size()); j++) {
int newmsk = 0;
for (int i = 0; i < (int)v2.size(); i++) if (j >> i & 1) newmsk ^= (1 << v2[i]);
res += a[newmsk];
}
cout << res << '\n';
continue;
}
}
}
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