2020 Mid-Atlantic USA Regional Contest

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2021-03-06 10:00 AKST

2020 Mid-Atlantic USA Regional Contest

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2021-03-06 15:00 AKST
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Problem J
Basic Basis

You are given a sequence of $n$ bit strings $b_1, b_2, \ldots , b_ n$, each with $k \times 4$ bits.

You are also given another sequence of $m$ bit strings $a_1, a_2, \ldots , a_ m$, each also with $k \times 4$ bits.

Let $f(x)$ denote the minimum index $i$ such that it is possible to take a non-empty subset of $b_1, b_2, \ldots , b_ i$, XOR them all together, and get $x$. If there is no such index, $f(x) = -1$.

Print the values $f(a_1), f(a_2), \ldots , f(a_ m)$.

Input

The first line of input contains three integers $n$ ($1 \le n \le 1\, 000$), $m$ ($1 \le m \le 1\, 000$) and $k$ ($1 \le k \le 40$), where $n$ is the length of sequence $b$, $m$ is the length of sequence $a$, and the elements of both sequences are bit strings with $k \times 4$ bits.

Each of the next $n$ lines contains a hexadecimal representation of $b_ i$ as a string of length $k$. The strings consist only of hexadecimal digits (‘0’–‘9’ and ‘a’–‘f’).

Then, each of the next $m$ lines contains a hexadecimal representation of $a_ i$ in the same format as above.

Output

Output $m$ lines with a single integer on each line, where the integer on the $i$th line is $f(a_ i)$.

Sample Input 1 Sample Output 1
3 5 2
02
e1
fa
02
e3
1b
e1
ff
1
2
3
2
-1
Sample Input 2 Sample Output 2
5 6 2
01
02
04
08
10
01
02
03
04
05
64
1
2
2
3
3
-1