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Math teacher's homework
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 490Accepted: 247


Mr. Furion is a math teacher. His students are very lazy and they do not like to do their homework. One day, Mr. Furion decides to give them a special problem in order to see whether his students are talents in math or they are just too lazy to do their homework. The problem is:

Given an integer k, n integers m1,m2…mn, and a formula below:
X1 xor X2 xor X3… xor Xn = k
Please figure out that how many integral solutions of the formula can satisfy:
0<=Xi<=mi (i=1…n)


There are at most 100 test cases.
The first line of each test case contains two integers, n and k. The second line of each test case contains n integers: m1,m2…mn. The meaning of n,k, m1,m2…mn are described above. (1<=n<=50,0<=k,m1,m2…mn<=231-1 )
The input is ended by “0 0”


You should output an integer for each test case, which is the number of solutions. As the number might be very large, you should only output the number modulo 1000000003.

Sample Input

11 2047
1024 512 256 128 64 32 16 8 4 2 1
10 2047
1024 512 256 128 64 32 16 8 4 2 
0 0

Sample Output



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