# Pku3986 Math teacher's homework

时间限制：10s 空间限制：128MB

### 题目描述

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 m

X

Please figure out that how many integral solutions of the formula can satisfy:

0<=X

Given an integer k, n integers m

_{1},m_{2}…m_{n}, and a formula below:X

_{1}xor X_{2}xor X_{3}… xor X_{n}= kPlease 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

### 输入格式

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: m

The input is ended by “0 0”

The first line of each test case contains two integers, n and k. The second line of each test case contains n integers: m

_{1},m_{2}…m_{n}. The meaning of n,k, m_{1},m_{2}…m_{n}are described above. (1<=n<=50,0<=k,m_{1},m_{2}…m_{n}<=2^{31}-1 )The input is ended by “0 0”

### 输出格式

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.

### 样例输入

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

### 样例输出

1 0

### 提示

没有写明提示

### 题目来源

没有写明来源