BADXOR  Bad XOR
Bad XOR  BADXOR
Time Limit: 1s
You are given an array A of N elements. Also you are given another array B of M elements. Any subset (i_{1}, i_{2}, i_{3}, …., i_{p }) is bad IFF ( Ai_{1} ⊕ Ai_{2} ⊕ …. ⊕ Ai_{p }) 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.
Input
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 <= A_{i }<=1000). The next line contains M integers of the array B (0 <= B_{i }<=1000). You can assume that each element of array B will be unique.
Output
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 2 3 1 2 0 1 2 1 3 1 0 1 2 
Case 1: 1 Case 2: 0

Problem Setter: Nafis Sadique
Special Thanks: Ahmad Faiyaz
hide comments
ayush5148:
20170815 21:25:05
Spoj toolkit for this question is WRONG .....


namitp:
20170813 08:18:59
How Best Soln is in 0.01......strange.... 

blackjack123:
20170729 14:08:02
commutative property of xor 

nk17kumar:
20170703 06:12:29
thanks to @yash_22 comment :) 

sas1905:
20170523 01:01:03
corner case n=0 

kg93999:
20170322 18:24:48
java tle


aman224:
20170316 09:26:05
Why modulo 100000007 and not 1000000007 ?


lonewolf_1:
20170228 11:31:14
10^8 + 7 modulo :)


yash_22:
20161228 08:25:37
@aditya730 the constraints are not wrong. If a XOR b = c, then it is possible that c > a && c > b. For example 999 XOR 24 = 1023. You need to consider only till 1023 because the bit corresponding to 2**10 i.e. 1024 will never be set in the input and the XOR will never exceed 1023 

aditya730:
20161227 20:30:34
The constraints are all wrong.even with an array of 1020 got wa. More than 2 hours wasted due to this.And spoj toolkit is wrong for this one.Assume number of elements are 1025 
Added by:  Faiyaz 
Date:  20131224 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 