Description

Bessie is leading the cows in an attempt to escape! To do this, the cows are sending secret binary messages to each other.

Ever the clever counterspy, Farmer John has intercepted the first $b_i$ ($1 \le b_i \le 10,000$) bits of each of $M$ ($1 \le M \le 50,000$) of these secret binary messages.

He has compiled a list of $N$ ($1 \le N \le 50,000$) partial codewords that he thinks the cows are using. Sadly, he only knows the first $c_j$ ($1 \le c_j \le 10,000$) bits of codeword $j$.

For each codeword $j$, he wants to know how many of the intercepted messages match that codeword (i.e., for codeword $j$, how many times does a message and the codeword have the same initial bits). Your job is to compute this number.

The total number of bits in the input (i.e., the sum of the $b_i$ and the $c_j$) will not exceed $500,000$.

Input Format

Line $1$: Two integers: $M$ and $N$.

Lines $2 \ldots M+1$: Line $i+1$ describes intercepted code $i$ with an integer $b_i$ followed by $b_i$ space-separated 0's and 1's.

Lines $M+2 \ldots M+N+1$: Line $M+j+1$ describes codeword $j$ with an integer $c_j$ followed by $c_j$ space-separated 0's and 1's.

Output Format

Lines $1 \ldots N$: Line $j$: The number of messages that the $j$-th codeword could match.

4 5 
3 0 1 0 
1 1 
3 1 0 0 
3 1 1 0 
1 0 
1 1 
2 0 1 
5 0 1 0 0 1 
2 1 1 

1 
3 
1 
1 
2 

Hint

Four messages; five codewords.

The intercepted messages start with 010, 1, 100, and 110.

The possible codewords start with 0, 1, 01, 01001, and 11.

0 matches only 010: 1 match

1 matches 1, 100, and 110: 3 matches

01 matches only 010: 1 match

01001 matches 010: 1 match

11 matches 1 and 110: 2 matches