#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef double dou;
#define pii pair<int, int>
#define fi first
#define se second
#define pb push_back
#define ALL(v) v.begin(), v.end()
#define BITJ(x, j) (((x)>>(j))&1)
#define MASK(j) (1LL<<(j))
template<typename T> bool maximize(T &x, const T &y) {
if (x < y) {x = y; return 1;}
return 0;
}
template<typename T> bool minimize(T &x, const T &y) {
if (x > y) {x = y; return 1;}
return 0;
}
const int maxn = 20;
int n;
int dp1[MASK(maxn)], dp2[MASK(maxn)], val[MASK(maxn)];
string s;
int ans;
void zeta() {
for (int j = 0; j < n; j++) {
for (int mask = 0; mask < MASK(n); mask++) {
if (BITJ(mask, j)) {
dp1[mask] += dp1[mask^MASK(j)];
}
}
for (int mask = MASK(n)-1; mask >= 0; mask--) {
if (!BITJ(mask, j)) {
dp2[mask] += dp2[mask^MASK(j)];
}
}
}
// for (int mask = 0; mask < MASK(n); mask++) {
// cout << bitset<3>(mask) << ' ' << dp1[mask] << "\n";
// }
}
void sinh0(int j, int mask, int cnt) {
if (j >= n) {
if (cnt&1) ans -= dp2[mask];
else ans += dp2[mask];
return;
}
if (s[j] == '0') {
sinh0(j+1, mask^MASK(n-j-1), cnt+1);
sinh0(j+1, mask, cnt);
}
else if (s[j] == '1') {
sinh0(j+1, mask^MASK(n-j-1), cnt);
}
else {
sinh0(j+1, mask, cnt);
}
}
void solvecase0() {
sinh0(0, 0, 0);
}
void sinh1(int j, int mask, int cnt) {
if (j >= n) {
// cout << (bitset<3>)mask << ' ' << cnt << "\n";
if (cnt&1) ans -= dp1[mask];
else ans += dp1[mask];
return;
}
if (s[j] == '0') {
sinh1(j+1, mask, cnt);
}
else if (s[j] == '1') {
sinh1(j+1, mask^MASK(n-j-1), cnt);
sinh1(j+1, mask, cnt+1);
}
else {
sinh1(j+1, mask^MASK(n-j-1), cnt);
}
}
void solvecase1() {
sinh1(0, 0, 0);
}
void sinhbruh(int j, int mask) {
if (j >= n) {
ans += val[mask];
return;
}
if (s[j] == '0') {
sinhbruh(j+1, mask);
}
else if (s[j] == '1') {
sinhbruh(j+1, mask^MASK(n-j-1));
}
else {
sinhbruh(j+1, mask^MASK(n-j-1));
sinhbruh(j+1, mask);
}
}
void solvecasebruh() {
sinhbruh(0, 0);
}
void solvequ(string s) {
int cnt0, cnt1, cntc;
cnt0 = cnt1 = cntc = 0;
for (int i = 0; i < n; i++) {
if (s[i] == '0') cnt0++;
else if (s[i] == '1') cnt1++;
else cntc++;
}
int temp = min({cnt0, cnt1, cntc});
ans = 0;
if (temp == cnt0) return solvecase0();
else if (temp == cnt1) return solvecase1();
else return solvecasebruh();
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
// #define name "task"
// if (fopen(name".inp", "r")) {
// freopen(name".inp", "r", stdin);
// freopen(name".out", "w", stdout);
// }
int q;
cin >> n >> q;
for (int i = 0; i < MASK(n); i++) {
char x;
cin >> x;
val[i] = x-'0';
dp1[i] = dp2[i] = val[i];
}
zeta();
cin.ignore();
while (q--) {
// cin.ignore();
getline(cin, s);
// cin.ignore();
// cout << s << "\n";
solvequ(s);
cout << ans << "\n";
}
}
/*
3 1
12345678
0??
3 2
12345678
000
0??
3 5
12345678
000
0??
1?0
?11
???
*/
