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;
#define fi first
#define se second
#define ll long long
#define mp(x, y) make_pair(x, y)
#define sz(v) ((int) (v).size())
#define all(v) (v).begin(), (v).end()
#define MASK(i) (1LL << (i))
#define BIT(x, y) (((x) >> (y)) & 1)
#define pb push_back
#define heap priority_queue
#define max_rng *max_element
#define min_rng *min_element
#define rep(i, n) for(int i = 1, _n = (n); i <= _n; ++i)
#define forn(i, a, b) for(int i = (a), _b = (b); i <= _b; ++i)
#define ford(i, a, b) for(int i = (a), _b = (b); i >= _b; --i)
template <class X, class Y>
inline bool maximize(X &x, Y y) {
return (x < y ? x = y, true : false);
}
template <class X, class Y>
inline bool minimize(X &x, Y y) {
return (x > y ? x = y, true : false);
}
template <class X>
inline void compress(vector<X> &a) {
sort(all(a));
a.resize(unique(all(a)) - a.begin());
}
int ctz(ll x) { return __builtin_ctzll(x); }
int lg(ll x) { return 63 - __builtin_clzll(x); }
int popcnt(ll x) { return __builtin_popcount(x); }
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) {
return l + abs((ll) rng()) % (r - l + 1);
}
const ll oo = (ll) 1e18 + 5;
const int inf = (ll) 1e9 + 7, mod = (ll) 1e9 + 7;
const int N = 21, LOG = 21;
void add(int &x, int y) { x += y; if (x >= mod) x -= mod; }
void sub(int &x, int y) { x -= y; if (x < 0) x += mod; }
int L, Q;
char cost[MASK(N) + 5];
ll f[MASK(N) + 5], dp[MASK(N) + 5];
int main(void) {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> L >> Q;
forn(i, 0, MASK(L) - 1) {
cin >> cost[i];
f[i] = dp[i] = cost[i] - '0';
}
forn(i, 0, L - 1) forn(msk, 0, MASK(L) - 1)
if (BIT(msk, i)) f[msk] += f[msk - MASK(i)];
forn(i, 0, L - 1) forn(msk, 0, MASK(L) - 1)
if (!BIT(msk, i)) dp[msk] += dp[msk + MASK(i)];
string s;
rep(_, Q) {
cin >> s;
int mask1 = 0, mask2 = 0, mask3 = 0;
forn(i, 0, L - 1) {
int cur = MASK(L - i - 1);
if (s[i] == '1')
mask1 += cur;
else if (s[i] == '?') mask2 += cur;
else mask3 += cur;
}
ll res = 0;
if (popcnt(mask2) <= 6) {
for (int msk = mask2; ; msk = (msk - 1) & mask2) {
res += cost[msk + mask1] - '0';
if (!msk) break;
}
}
else if (popcnt(mask1) <= 6) {
for (int msk = mask1; ; msk = (msk - 1) & mask1) {
if (popcnt(msk) & 1) res -= dp[msk + mask2];
else res += dp[msk + mask2];
if (!msk) break;
}
}
else {
for (int msk = mask3; ; msk = (msk - 1) & mask3) {
if (popcnt(msk) & 1) res -= dp[msk + mask1];
else res += dp[msk + mask1];
if (!msk) break;
}
}
cout << res << '\n';
}
return 0;
}
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