Determinant Strikes Back

Dinara has an integer $x$ and two $n$ arrays $a\_1, \dots, a\_n$, $b\_1, \dots, b\_n$. She makes an $n \times n$ matrix $M$ where

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 the matrix $M$ 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 an integer which denotes the result.

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