Zeroing a Binary Sequence

Adam likes solving challenges. He is given a binary sequence of length $N$.

Adam makes exactly $K$ moves. On each move he picks one element of the sequence and flips it, so a 0 becomes 1 and a 1 becomes 0. After all $K$ moves the sequence must contain only zeroes.

Adam solves this easily, but he wants to know how many ways there are. Print the number of ways modulo $10^9 + 7$.

Two ways count as different if there is an $i$ such that they pick different elements on the $i$-th move.

The first line contains an integer $T$ ($1 \le T \le 50$), the number of test cases. The $T$ test cases follow.

The first line of each test case contains two integers $N$ ($1 \le N \le 1000$) and $K$ ($1 \le K \le 1000$), separated by a space. $N$ is the length of the sequence and $K$ is the number of moves. Each of the next $N$ lines contains 0 or 1, one element of the sequence, given in the order of the sequence.

For each test case, print one line in the form Case #X: Y, where $X$ is the test case number starting from 1 and $Y$ is the number of ways modulo $10^9 + 7$.