Solution required in python only Given a triplet of integers (X , Y , Z), such that X ≤ Y and Y ≥ Z, we define f(X , Y , Z) to be (X + Y) * (Y + Z). If either X > Y or Y < Z, or both, then f(X , Y , Z) is defined to be 0. You are provided three arrays A , B and C of any length (their lengths may or may not be equal). Your task is to find the sum of f(X , Y , Z) over all triplets (X, Y , Z) where X, Y and Z belong to A, B and C respectively. Output your sum for each test case modulo 1000000007. Input The first line contains a single integer, T, which is the number of test cases. The description of each testcase follows: The first line of each testcase contains 3 integers: p, q and r. These denote the lengths of A,B and C respectively. The second line contains p integers, which are the elements of A The third line contains q integers, which are the elements of B The fourth line contains r integers, which are the elements of C Output Output the required sum modulo 1000000007 for each test case in a new line.   Example : Input: 1 3 1 3 1 2 3 5 4 5 6 Output: 399

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Solution required in python only

Given a triplet of integers (X , Y , Z), such that X ≤ Y and Y ≥ Z, we define f(X , Y , Z) to be (X + Y) * (Y + Z). If either X > Y or Y < Z, or both, then f(X , Y , Z) is defined to be 0.

You are provided three arrays A , B and of any length (their lengths may or may not be equal).

Your task is to find the sum of f(X , Y , Z) over all triplets (X, Y , Z) where X, Y and belong to AB and C respectively.

Output your sum for each test case modulo 1000000007.

Input

  • The first line contains a single integer, T, which is the number of test cases. The description of each testcase follows:
  • The first line of each testcase contains 3 integers: p, q and r. These denote the lengths of A,B and C respectively.
  • The second line contains p integers, which are the elements of A
  • The third line contains q integers, which are the elements of B
  • The fourth line contains r integers, which are the elements of C

Output

Output the required sum modulo 1000000007 for each test case in a new line.

 

Example :

Input: 1

3 1 3

1 2 3

5

4 5 6

Output: 399

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