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

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

He has compiled a list of N (1 <= N <= 50,000) partial codewords that he thinks the cows are using. Sadly, he only knows the first c_j (1 <= c_j <= 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.

입력 형식

• Line 1: Two integers: M and N
• Lines 2..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..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

출력 형식

• Lines 1..N: Line j: The number of messages that the jth codeword could match.

예제 입력

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

예제 출력

1
3
1
1
2

힌트

• 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