This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast,unroll-loops")
// #pragma comment(linker, "/stack:200000000")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma,tune=native")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef int ll;
typedef long double ld;
typedef pair <ll, ll> pll;
#ifdef SINA
#define dbg(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << std::endl; }
template <typename Arg1, typename... Args> void __f (const char* names, Arg1&& arg1, Args&&... args) {
const char* comma = strchr(names + 1, ',');cout.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...); }
#define dbg2(x, j, n) cout<< #x << " : "; output((j), (n), x, 1); cout.flush();
#else
#define dbg(...) 0
#define dbg2(x, j, n) 0
#endif
#define SZ(x) ((ll)((x).size()))
#define File(s, t) freopen(s ".txt", "r", stdin); freopen(t ".txt", "w", stdout);
#define input(j, n, a) for (int _i = (j); _i < (n)+(j); _i++) cin>> a[_i];
#define output(j, n, a, t) for (int _i = (j); _i < (n)+(j); _i++) cout<< a[_i] << (((t) && _i != (n)+(j)-1)? ' ' : '\n');
#define kill(x) return cout<< x << endl, 0
#define cl const ll
#define fr first
#define sc second
#define lc (v << 1)
#define rc (lc | 1)
#define mid ((l + r) >> 1)
#define All(x) (x).begin(), (x).end()
cl inf = sizeof(ll) == 4 ? (1e9 + 10) : (3e18), mod = 1e9 + 7, MOD = 998244353;
template <class A,class B> ostream& operator << (ostream& out,const pair<A,B>&a){return out<<'('<<a.first<<", "<<a.second<<')';}
template <class A> ostream& operator << (ostream& out, const vector<A> &a) {
out<< '['; for (int i = -1; ++i < int(a.size());) out<< a[i] << (i + 1 < int(a.size()) ? ", " : ""); return out<<']'; }
template <class T, typename _t = less <T> > using Tree = tree <T, null_type, _t, rb_tree_tag, tree_order_statistics_node_update>;
cl L = 20, N = 1 << L;
ll a [N], dp0 [N], dp1 [N], n, q, ans;
char c;
#define C(x) __builtin_popcount(x)
#define f(x) ((~(x)) & ((1 << n) - 1))
int main ()
{
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
cin>> n >> q;
for (ll i = 0; i < (1 << n); i++) cin>> c, dp0[i] = dp1[i] = a[i] = c - '0';
for (ll i = 0; i < L; i++) for (ll msk = 0; msk < (1 << n); msk++) {
if (msk >> i & 1) dp1[msk] += dp1[msk ^ (1 << i)];
else dp0[msk] += dp0[msk ^ (1 << i)];
}
for (ll msk0 = 0, msk1 = 0, msk2 = 0, msk; q--; msk0 = msk1 = msk2 = 0) {
for (ll i = 0; i < n; i++) {
cin>> c;
msk0 = (msk0 << 1) | (c == '0');
msk1 = (msk1 << 1) | (c == '1');
msk2 = (msk2 << 1) | (c == '?');
}
if (C(msk2) < 7)
for (msk = msk2, ans = a[msk1]; msk; msk = (msk - 1) & msk2) ans += a[msk1 | msk];
else if (C(msk1) < 7)
for (msk = msk1, ans = dp1[msk1 | msk2]; msk; msk = (msk - 1) & msk1) ans += (C(msk) & 1 ? -1 : 1) * dp1[msk2 | (msk1 ^ msk)];
else
for (msk = msk0, ans = dp0[msk1]; msk; msk = (msk - 1) & msk0) ans += (C(msk) & 1 ? -1 : 1) * dp0[msk1 | msk];
cout<< ans << ' ' << '\n';
}
cerr<< "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
return 0;
}
/*
3 5
12345678
000
0??
1?0
?11
???
4 8
3141592653589793
0101
?01?
??1?
?0??
1?00
01?1
??10
????
*/
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