#include<iostream>
#include<stack>
#include<map>
#include<vector>
#include<string>
#include<unordered_map>
#include <queue>
#include<cstring>
#include<limits.h>
#include <cassert>
#include<cmath>
#include<set>
#include<algorithm>
#include <iomanip>
#include<numeric> //gcd(a,b)
#include<bitset>
#include <cstdlib>
#include <cstdint>
using namespace std;
#define ll long long
#define f first
//#define endl "\n"
#define s second
#define pii pair<int,int>
#define ppii pair<int,pii>
#define vi vector<int>
#define pb push_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define F(n) for(int i=0;i<n;i++)
#define lb lower_bound
#define ub upper_bound
#define fastio ios::sync_with_stdio(false);cin.tie(NULL);
#pragma GCC optimize ("03,unroll-loops")
using namespace std;
#define int long long
#define double long double
const int mod=998244353,mxn=3e5+5,lg=60,inf=1e18,minf=-1e18,Mxn=1e6+50000;
int dp1[Mxn+10],dp0[Mxn+10],cost[Mxn+10];
int32_t main(){
fastio
int n,q;cin>>n>>q;
string a;cin>>a;
for(int i=0;i<(1LL<<n);i++)cost[i]=dp1[i]=dp0[i]=(a[i]-'0');
for(int i=0;i<n;i++)for(int j=0;j<(1LL<<n);j++)if(j&(1LL<<i))dp1[j]+=dp1[j^(1LL<<i)];
for(int i=0;i<n;i++)for(int j=(1LL<<n)-1;j>=0;j--)if(!(j&(1LL<<i)))dp0[j]+=dp0[j+(1LL<<i)];
while(q--){
cin>>a;
reverse(all(a));
int x=0,y=0;
vector<int>o,z,c;
for(int i=0;i<n;i++){
if(a[i]=='1')x+=(1LL<<i),o.pb(i),y+=(1LL<<i);
else if(a[i]=='?')x+=(1LL<<i),c.pb(i);
else z.pb(i);
}
int m=0;
int ans=0;
if(c.size()<=5){
m=c.size();
for(int i=0;i<(1LL<<m);i++){
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x-=(1LL<<c[j]);
ans+=cost[x];
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x+=(1LL<<c[j]);
}
}
else if(o.size()<z.size()){
ans=dp1[x];
m=o.size();
for(int i=0;i<(1LL<<m)-1;i++){
int cnt=0;
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x-=(1LL<<o[j]),cnt++;
if(cnt%2)ans-=dp1[x];
else ans+=dp1[x];
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x+=(1LL<<o[j]);
}
/*
*/
}
else{
ans=dp0[y];
m=z.size();
for(int i=1;i<(1LL<<m);i++){
int cnt=0;
for(int j=0;j<m;j++)if((i&(1LL<<j)))y+=(1LL<<z[j]),cnt++;
if(cnt%2)ans-=dp0[y];
else ans+=dp0[y];
for(int j=0;j<m;j++)if((i&(1LL<<j)))y-=(1LL<<z[j]);
}
/*
*/
}
cout<<ans<<'\n';
//return 0;
//cout<<dp1[x]<<" "<<dp0[y]<<'\n';
}
}
/*
if cnt? <= sqrt(m) we can do (2^4)? bruteforce (maybe even 5)
else we can do sos dp and somehow remove the overcount
we can turn all ? into one and get sos of that bit
overcount when "1" bit that is originaly turned on switch to 0(for subset)
we can switch them off and subtract from the original answer so it cost 2^(cnt1){
we need to somehow do pie
starting from original answer-> if we turn off 1 bit
ans-(turn of x bit)-(turn of y bit)+(turn of x and y bit)
so if cnt%2==1 then we subtract
else we add back in
}
cnt1 can be at most 16,worst case is all 1 (2^16)
we can also do sos dp where 0 is now the "switchable" value
so if cnt0<cnt1 we take do from 0 dp else from 1
tc-> worst case q*(2^m)*m
pre com time is m*(2^m+1)
q*(x*(2^x)+(2^(m-x)/2))
*/
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
4444 KB |
Output is correct |
2 |
Correct |
1 ms |
4444 KB |
Output is correct |
3 |
Correct |
1 ms |
4444 KB |
Output is correct |
4 |
Correct |
2 ms |
4444 KB |
Output is correct |
5 |
Correct |
1 ms |
4444 KB |
Output is correct |
6 |
Correct |
1 ms |
4444 KB |
Output is correct |
7 |
Correct |
2 ms |
4700 KB |
Output is correct |
8 |
Correct |
1 ms |
4444 KB |
Output is correct |
9 |
Correct |
1 ms |
4440 KB |
Output is correct |
10 |
Correct |
1 ms |
4440 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
4444 KB |
Output is correct |
2 |
Correct |
1 ms |
4444 KB |
Output is correct |
3 |
Correct |
1 ms |
4444 KB |
Output is correct |
4 |
Correct |
2 ms |
4444 KB |
Output is correct |
5 |
Correct |
1 ms |
4444 KB |
Output is correct |
6 |
Correct |
1 ms |
4444 KB |
Output is correct |
7 |
Correct |
2 ms |
4700 KB |
Output is correct |
8 |
Correct |
1 ms |
4444 KB |
Output is correct |
9 |
Correct |
1 ms |
4440 KB |
Output is correct |
10 |
Correct |
1 ms |
4440 KB |
Output is correct |
11 |
Correct |
730 ms |
19284 KB |
Output is correct |
12 |
Correct |
501 ms |
18772 KB |
Output is correct |
13 |
Correct |
468 ms |
18000 KB |
Output is correct |
14 |
Correct |
472 ms |
18248 KB |
Output is correct |
15 |
Correct |
400 ms |
19212 KB |
Output is correct |
16 |
Correct |
555 ms |
18308 KB |
Output is correct |
17 |
Correct |
600 ms |
18216 KB |
Output is correct |
18 |
Correct |
259 ms |
20160 KB |
Output is correct |
19 |
Correct |
368 ms |
17184 KB |
Output is correct |
20 |
Correct |
492 ms |
18772 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
4444 KB |
Output is correct |
2 |
Correct |
1 ms |
4444 KB |
Output is correct |
3 |
Correct |
1 ms |
4444 KB |
Output is correct |
4 |
Correct |
2 ms |
4444 KB |
Output is correct |
5 |
Correct |
1 ms |
4444 KB |
Output is correct |
6 |
Correct |
1 ms |
4444 KB |
Output is correct |
7 |
Correct |
2 ms |
4700 KB |
Output is correct |
8 |
Correct |
1 ms |
4444 KB |
Output is correct |
9 |
Correct |
1 ms |
4440 KB |
Output is correct |
10 |
Correct |
1 ms |
4440 KB |
Output is correct |
11 |
Correct |
730 ms |
19284 KB |
Output is correct |
12 |
Correct |
501 ms |
18772 KB |
Output is correct |
13 |
Correct |
468 ms |
18000 KB |
Output is correct |
14 |
Correct |
472 ms |
18248 KB |
Output is correct |
15 |
Correct |
400 ms |
19212 KB |
Output is correct |
16 |
Correct |
555 ms |
18308 KB |
Output is correct |
17 |
Correct |
600 ms |
18216 KB |
Output is correct |
18 |
Correct |
259 ms |
20160 KB |
Output is correct |
19 |
Correct |
368 ms |
17184 KB |
Output is correct |
20 |
Correct |
492 ms |
18772 KB |
Output is correct |
21 |
Correct |
399 ms |
22460 KB |
Output is correct |
22 |
Correct |
513 ms |
22672 KB |
Output is correct |
23 |
Correct |
646 ms |
21580 KB |
Output is correct |
24 |
Correct |
625 ms |
21332 KB |
Output is correct |
25 |
Correct |
434 ms |
23232 KB |
Output is correct |
26 |
Correct |
655 ms |
21752 KB |
Output is correct |
27 |
Correct |
651 ms |
21784 KB |
Output is correct |
28 |
Correct |
264 ms |
24380 KB |
Output is correct |
29 |
Correct |
389 ms |
20308 KB |
Output is correct |
30 |
Correct |
488 ms |
22532 KB |
Output is correct |
31 |
Correct |
525 ms |
22404 KB |
Output is correct |
32 |
Correct |
789 ms |
22328 KB |
Output is correct |
33 |
Correct |
531 ms |
21200 KB |
Output is correct |
34 |
Correct |
629 ms |
21228 KB |
Output is correct |
35 |
Correct |
649 ms |
21836 KB |
Output is correct |
36 |
Correct |
279 ms |
20124 KB |
Output is correct |
37 |
Correct |
411 ms |
22284 KB |
Output is correct |
38 |
Correct |
408 ms |
20304 KB |
Output is correct |
39 |
Correct |
636 ms |
21324 KB |
Output is correct |
40 |
Correct |
629 ms |
21280 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
4444 KB |
Output is correct |
2 |
Correct |
1 ms |
4444 KB |
Output is correct |
3 |
Correct |
1 ms |
4444 KB |
Output is correct |
4 |
Correct |
2 ms |
4444 KB |
Output is correct |
5 |
Correct |
1 ms |
4444 KB |
Output is correct |
6 |
Correct |
1 ms |
4444 KB |
Output is correct |
7 |
Correct |
2 ms |
4700 KB |
Output is correct |
8 |
Correct |
1 ms |
4444 KB |
Output is correct |
9 |
Correct |
1 ms |
4440 KB |
Output is correct |
10 |
Correct |
1 ms |
4440 KB |
Output is correct |
11 |
Correct |
67 ms |
28660 KB |
Output is correct |
12 |
Correct |
56 ms |
28408 KB |
Output is correct |
13 |
Correct |
74 ms |
28432 KB |
Output is correct |
14 |
Correct |
103 ms |
28404 KB |
Output is correct |
15 |
Correct |
74 ms |
28540 KB |
Output is correct |
16 |
Correct |
110 ms |
28404 KB |
Output is correct |
17 |
Correct |
108 ms |
28404 KB |
Output is correct |
18 |
Correct |
42 ms |
28472 KB |
Output is correct |
19 |
Correct |
54 ms |
28292 KB |
Output is correct |
20 |
Correct |
65 ms |
28532 KB |
Output is correct |
21 |
Correct |
72 ms |
28404 KB |
Output is correct |
22 |
Correct |
101 ms |
28404 KB |
Output is correct |
23 |
Correct |
78 ms |
28404 KB |
Output is correct |
24 |
Correct |
142 ms |
28528 KB |
Output is correct |
25 |
Correct |
108 ms |
28404 KB |
Output is correct |
26 |
Correct |
41 ms |
28148 KB |
Output is correct |
27 |
Correct |
64 ms |
28412 KB |
Output is correct |
28 |
Correct |
55 ms |
28148 KB |
Output is correct |
29 |
Correct |
86 ms |
28512 KB |
Output is correct |
30 |
Correct |
147 ms |
28440 KB |
Output is correct |
31 |
Correct |
61 ms |
28400 KB |
Output is correct |
32 |
Correct |
114 ms |
28472 KB |
Output is correct |
33 |
Correct |
113 ms |
28408 KB |
Output is correct |
34 |
Correct |
44 ms |
28276 KB |
Output is correct |
35 |
Correct |
104 ms |
28404 KB |
Output is correct |
36 |
Correct |
104 ms |
28492 KB |
Output is correct |
37 |
Correct |
105 ms |
28508 KB |
Output is correct |
38 |
Correct |
89 ms |
28296 KB |
Output is correct |
39 |
Correct |
123 ms |
28404 KB |
Output is correct |
40 |
Correct |
88 ms |
28288 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
4444 KB |
Output is correct |
2 |
Correct |
1 ms |
4444 KB |
Output is correct |
3 |
Correct |
1 ms |
4444 KB |
Output is correct |
4 |
Correct |
2 ms |
4444 KB |
Output is correct |
5 |
Correct |
1 ms |
4444 KB |
Output is correct |
6 |
Correct |
1 ms |
4444 KB |
Output is correct |
7 |
Correct |
2 ms |
4700 KB |
Output is correct |
8 |
Correct |
1 ms |
4444 KB |
Output is correct |
9 |
Correct |
1 ms |
4440 KB |
Output is correct |
10 |
Correct |
1 ms |
4440 KB |
Output is correct |
11 |
Correct |
730 ms |
19284 KB |
Output is correct |
12 |
Correct |
501 ms |
18772 KB |
Output is correct |
13 |
Correct |
468 ms |
18000 KB |
Output is correct |
14 |
Correct |
472 ms |
18248 KB |
Output is correct |
15 |
Correct |
400 ms |
19212 KB |
Output is correct |
16 |
Correct |
555 ms |
18308 KB |
Output is correct |
17 |
Correct |
600 ms |
18216 KB |
Output is correct |
18 |
Correct |
259 ms |
20160 KB |
Output is correct |
19 |
Correct |
368 ms |
17184 KB |
Output is correct |
20 |
Correct |
492 ms |
18772 KB |
Output is correct |
21 |
Correct |
399 ms |
22460 KB |
Output is correct |
22 |
Correct |
513 ms |
22672 KB |
Output is correct |
23 |
Correct |
646 ms |
21580 KB |
Output is correct |
24 |
Correct |
625 ms |
21332 KB |
Output is correct |
25 |
Correct |
434 ms |
23232 KB |
Output is correct |
26 |
Correct |
655 ms |
21752 KB |
Output is correct |
27 |
Correct |
651 ms |
21784 KB |
Output is correct |
28 |
Correct |
264 ms |
24380 KB |
Output is correct |
29 |
Correct |
389 ms |
20308 KB |
Output is correct |
30 |
Correct |
488 ms |
22532 KB |
Output is correct |
31 |
Correct |
525 ms |
22404 KB |
Output is correct |
32 |
Correct |
789 ms |
22328 KB |
Output is correct |
33 |
Correct |
531 ms |
21200 KB |
Output is correct |
34 |
Correct |
629 ms |
21228 KB |
Output is correct |
35 |
Correct |
649 ms |
21836 KB |
Output is correct |
36 |
Correct |
279 ms |
20124 KB |
Output is correct |
37 |
Correct |
411 ms |
22284 KB |
Output is correct |
38 |
Correct |
408 ms |
20304 KB |
Output is correct |
39 |
Correct |
636 ms |
21324 KB |
Output is correct |
40 |
Correct |
629 ms |
21280 KB |
Output is correct |
41 |
Correct |
67 ms |
28660 KB |
Output is correct |
42 |
Correct |
56 ms |
28408 KB |
Output is correct |
43 |
Correct |
74 ms |
28432 KB |
Output is correct |
44 |
Correct |
103 ms |
28404 KB |
Output is correct |
45 |
Correct |
74 ms |
28540 KB |
Output is correct |
46 |
Correct |
110 ms |
28404 KB |
Output is correct |
47 |
Correct |
108 ms |
28404 KB |
Output is correct |
48 |
Correct |
42 ms |
28472 KB |
Output is correct |
49 |
Correct |
54 ms |
28292 KB |
Output is correct |
50 |
Correct |
65 ms |
28532 KB |
Output is correct |
51 |
Correct |
72 ms |
28404 KB |
Output is correct |
52 |
Correct |
101 ms |
28404 KB |
Output is correct |
53 |
Correct |
78 ms |
28404 KB |
Output is correct |
54 |
Correct |
142 ms |
28528 KB |
Output is correct |
55 |
Correct |
108 ms |
28404 KB |
Output is correct |
56 |
Correct |
41 ms |
28148 KB |
Output is correct |
57 |
Correct |
64 ms |
28412 KB |
Output is correct |
58 |
Correct |
55 ms |
28148 KB |
Output is correct |
59 |
Correct |
86 ms |
28512 KB |
Output is correct |
60 |
Correct |
147 ms |
28440 KB |
Output is correct |
61 |
Correct |
61 ms |
28400 KB |
Output is correct |
62 |
Correct |
114 ms |
28472 KB |
Output is correct |
63 |
Correct |
113 ms |
28408 KB |
Output is correct |
64 |
Correct |
44 ms |
28276 KB |
Output is correct |
65 |
Correct |
104 ms |
28404 KB |
Output is correct |
66 |
Correct |
104 ms |
28492 KB |
Output is correct |
67 |
Correct |
105 ms |
28508 KB |
Output is correct |
68 |
Correct |
89 ms |
28296 KB |
Output is correct |
69 |
Correct |
123 ms |
28404 KB |
Output is correct |
70 |
Correct |
88 ms |
28288 KB |
Output is correct |
71 |
Correct |
549 ms |
52752 KB |
Output is correct |
72 |
Correct |
586 ms |
52920 KB |
Output is correct |
73 |
Correct |
920 ms |
51388 KB |
Output is correct |
74 |
Correct |
1442 ms |
51880 KB |
Output is correct |
75 |
Correct |
624 ms |
53668 KB |
Output is correct |
76 |
Correct |
1678 ms |
52232 KB |
Output is correct |
77 |
Correct |
1695 ms |
51996 KB |
Output is correct |
78 |
Correct |
341 ms |
56052 KB |
Output is correct |
79 |
Correct |
555 ms |
49672 KB |
Output is correct |
80 |
Correct |
562 ms |
52784 KB |
Output is correct |
81 |
Correct |
882 ms |
52720 KB |
Output is correct |
82 |
Correct |
1448 ms |
51736 KB |
Output is correct |
83 |
Correct |
748 ms |
50948 KB |
Output is correct |
84 |
Execution timed out |
2027 ms |
51148 KB |
Time limit exceeded |
85 |
Halted |
0 ms |
0 KB |
- |