Time Limit: 1s

You are given an array A of N elements. Also you are given another array B of M elements. Any subset (i­1, i2, i3, …., ip ) is bad IFF ( Ai1 ⊕ Ai2 ⊕ …. ⊕ Aip ) equals any value of B. ⊕ means Bitwise XOR, which can be found with ^ syntax in popular programming languages. Now your job is to find the number of good subsets. Empty Subset has XOR value of 0.



The first line of input denotes the number of test cases T (1 <= T <= 20). The first line of each test case contains two integers N and M ( 0 <= N, M <= 1000). The next line contains N integers of the array A (0 <= Ai <=1000). The next line contains M integers of the array B (0 <= Bi <=1000). You can assume that each element of array B will be unique.  



For each case, print the case number and the total numbers of good subsets in a line. As the result can be very big, output it modulo 100000007.


                                Sample Input

Output for Sample Input


2 3

1 2

0 1 2

1 3


0 1 2

Case 1: 1

Case 2: 0



 Problem Setter: Nafis Sadique

Special Thanks: Ahmad Faiyaz

hide comments
maratha: 2019-08-12 11:09:59

Don't forget to reset array B.

dhruv2212000: 2019-03-21 00:35:03

Awesome problem! Instead of finding good subsets find bad subsets and subtract them from total number of subsets :)

ab_biswas09: 2019-03-20 22:33:12

MY 100th

mammadbastar: 2019-02-14 13:55:43

ba tashakor az ostad azizam kianoosh.a

ankitpriyarup: 2018-12-24 10:36:17

Nice question took me time to crack

pallindromeguy: 2018-07-12 23:53:46

Make sure your dp array is of size 1024, gave WA on 1007. And keep in mind the sample output. Rest is easy ;)

pk845: 2018-07-12 19:27:55

is there is new line after every test cases?
answer : "NO" !
wasted a lot of time :(

manktbvh11: 2018-06-06 17:33:50

carefully with mod . 1e8+7 not 1e9+7 . lmaoez

sherlock11: 2018-06-06 08:19:40

check case when n=0..........costed me plenty of wrong answers and lots of hour of remorse.......

Last edit: 2018-06-06 08:19:59
aman_sachin200: 2018-05-24 21:30:07

Read the modulo and the output format carefully!Cost me 4 WAs :(

Added by:Faiyaz
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64