This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//khodaya khodet komak kon
# include <bits/stdc++.h>
/*
// ordered_set
# include <ext/pb_ds/assoc_container.hpp>
# include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
# define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
*/
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef pair <pii, int> ppi;
typedef pair <int, pii> pip;
typedef pair <pii, pii> ppp;
typedef pair <ll, ll> pll;
# define A first
# define B second
# define endl '\n'
# define sep ' '
# define lc id << 1
# define rc lc | 1
# define all(x) x.begin(), x.end()
# define kill(x) return cout << x << endl, 0
# define SZ(x) int(x.size())
# define InTheNameOfGod ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
ll power(ll a, ll b, ll md) {return (!b ? 1 : (b & 1 ? a * power(a * a % md, b / 2, md) % md : power(a * a % md, b / 2, md) % md));}
const int xn = 21;
const int xm = - 20 + 10;
const int sq = 320;
const ll inf = 1e18 + 10;
const ll INF = 1e18 + 10;
const int mod = 998244353;
const int base = 257;
int n, q, a[1 << xn], cnt[3], ted[1 << xn];
pii dp[1 << xn];
string s;
void solve3(){
int mask = 0, tot = 0, ans = 0;
for (int i = 0; i < n; ++ i){
if (s[i] == '?')
mask += (1 << i);
else
tot += (s[i] - '0') * (1 << i);
}
for (int sub = mask; sub > 0; sub = ((sub - 1) & mask))
ans += a[tot + sub];
ans += a[tot];
cout << ans << endl;
}
void solve2(){
int tot = 0, ans = 0, mask = 0;
for (int i = 0; i < n; ++ i){
if (s[i] != '0')
tot += (1 << i);
if (s[i] == '1')
mask += (1 << i);
}
ans = dp[tot].A;
for (int sub = mask; sub > 0; sub = ((sub - 1) & mask)){
if (ted[sub] % 2)
ans -= dp[tot - sub].A;
else
ans += dp[tot - sub].A;
}
cout << ans << endl;
}
void solve1(){
int tot = 0, ans = 0, mask = 0;
for (int i = 0; i < n; ++ i){
if (s[i] == '1')
tot += (1 << i);
else if (s[i] == '0')
mask += (1 << i);
}
ans = dp[tot].B;
for (int sub = mask; sub > 0; sub = ((sub - 1) & mask)){
if (ted[sub] % 2)
ans -= dp[tot + sub].B;
else
ans += dp[tot + sub].B;
}
cout << ans << endl;
}
int main(){
InTheNameOfGod;
cin >> n >> q >> s;
for (int i = 0; i < (1 << n); ++ i)
a[i] = dp[i].A = dp[i].B = s[i] - '0';
for (int bit = 0; bit < n; ++ bit){
for (int mask = (1 << n) - 1; mask >= 0; -- mask)
if ((mask & (1 << bit)))
dp[mask].A += dp[mask - (1 << bit)].A;
for (int mask = 0; mask < (1 << n); ++ mask)
if (!(mask & (1 << bit)))
dp[mask].B += dp[mask + (1 << bit)].B;
}
for (int mask = 1; mask < (1 << n); ++ mask)
ted[mask] = ted[mask - (mask & - mask)] ^ 1;
while (q --){
cin >> s, reverse(all(s));
cnt[0] = cnt[1] = cnt[2] = 0;
for (char c : s){
if (c == '0')
++ cnt[0];
else if (c == '1')
++ cnt[1];
else
++ cnt[2];
}
if (cnt[0] <= n / 3)
solve1();
else if (cnt[1] <= n / 3)
solve2();
else
solve3();
}
return 0;
}
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