Pku3986 Math teacher's homework

内存限制：128 MiB 时间限制：10 Sec

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…m_n, and a formula below:
X₁ xor X₂ xor X₃… xor X_n = k
Please figure out that how many integral solutions of the formula can satisfy:
0<=X_i<=m_i (i=1…n)

给出两个整数K，N和一个整数序列M1,M2...Mn
求满足X1 Xor X2 Xor X3...Xor Xn=k且0<=Xi<=Mi（i=1...n)的解的个数

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…m_n. The meaning of n,k, m₁,m₂…m_n are described above. (1<=n<=50,0<=k,m₁,m₂…m_n<=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.

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			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

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#2992. Pku3986 Math teacher's homework

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