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;
int a[1048580], b[1048580], c[1048580];
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n, m;
cin >> n >> m;
for (int i=0; i<(1<<n); i++)
{
char x;
cin >> x;
a[i]=b[i]=c[i^((1<<n)-1)]=x-'0';
}
for (int i=0; i<n; i++)
for (int j=0; j<(1<<n); j++)
if (j&(1<<i))
b[j]+=b[j^(1<<i)], c[j]+=c[j^(1<<i)];
for (int i=0; i<m; i++)
{
string s;
cin >> s;
reverse(s.begin(), s.end());
vector<int> v0, v1, v2;
for (int j=0; j<n; j++)
{
if (s[j]=='0')
v0.push_back(j);
else if (s[j]=='1')
v1.push_back(j);
else
v2.push_back(j);
}
if (v0.size()<=v1.size() && v0.size()<=v2.size())
{
int x=0, sz=v0.size(), ans=0;
for (int j=0; j<n; j++)
if (s[j]=='0' || s[j]=='?')
x^=(1<<j);
for (int j=0; j<(1<<sz); j++)
{
int y=0, cnt=0;
for (int k=0; k<sz; k++)
{
if (j&(1<<k))
{
y^=(1<<v0[k]);
cnt++;
}
}
if (cnt&1)
ans-=c[x^y];
else
ans+=c[x^y];
}
cout << ans << '\n';
}
else if (v1.size()<=v0.size() && v1.size()<=v2.size())
{
int x=0, sz=v1.size(), ans=0;
for (int j=0; j<n; j++)
if (s[j]=='1' || s[j]=='?')
x^=(1<<j);
for (int j=0; j<(1<<sz); j++)
{
int y=0, cnt=0;
for (int k=0; k<sz; k++)
{
if (j&(1<<k))
{
y^=(1<<v1[k]);
cnt++;
}
}
if (cnt&1)
ans-=b[x^y];
else
ans+=b[x^y];
}
cout << ans << '\n';
}
else
{
int x=0, sz=v2.size(), ans=0;
for (int j=0; j<n; j++)
if (s[j]=='1')
x^=(1<<j);
for (int j=0; j<(1<<sz); j++)
{
int y=0;
for (int k=0; k<sz; k++)
if (j&(1<<k))
y^=(1<<v2[k]);
ans+=a[x^y];
}
cout << ans << '\n';
}
}
}
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