Determinant Strikes Back

Dinara has an integer $x$ and two arrays of length $n$, $a_1, \dots, a_n$ and $b_1, \dots, b_n$. She builds an $n \times n$ matrix $M$ as follows.

$M_{i, j} = \left\{\begin{matrix} x + a_i b_j & \mathrm{when}\ i = j \\ a_i b_j & \mathrm{otherwise} \end{matrix}\right.$

Find the determinant of $M$ modulo $(10^9+7)$.

The input consists of several test cases, terminated by end-of-file.

The first line of each test case contains two integers $n$ and $x$. The second line contains $n$ integers $a_1, \dots, a_n$. The third line contains $n$ integers $b_1, \dots, b_n$.

For each test case, print one integer, the result, on a line.

• $1 \leq n \leq 10^5$
• $0 \leq x, a_i, b_i \leq 10^9$
• The sum of $n$ does not exceed $10^6$.