Determinant

题号：NC213131
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Bobo has an integer x and two n arrays $a_1, \dots, a_n$ , $b_1, \dots, b_n$ . He 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 $(10^9+7)$ .

输入描述:

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 . The third line contains n integers .

* 
* 
* The sum of n does not exceed .

输出描述:

For each test case, print an integer which denotes the result.

示例1

输入

复制

2 1
0 0
0 0
2 1
1000000000 1000000000
1000000000 1000000000
3 2
2 3 3
2 3 3

输出

复制

1
99
96