CHOCOLA  Chocolate
We are given a bar of chocolate composed of m*n square pieces. One should break the chocolate into single squares. Parts of the chocolate may be broken along the vertical and horizontal lines as indicated by the broken lines in the picture.
A single break of a part of the chocolate along a chosen vertical or horizontal line divides that part into two smaller ones. Each break of a part of the chocolate is charged a cost expressed by a positive integer. This cost does not depend on the size of the part that is being broken but only depends on the line the break goes along. Let us denote the costs of breaking along consecutive vertical lines with x_{1}, x_{2}, ..., x_{m1} and along horizontal lines with y_{1}, y_{2}, ..., y_{n1}.
The cost of breaking the whole bar into single squares is the sum of the successive breaks. One should compute the minimal cost of breaking the whole chocolate into single squares.
For example, if we break the chocolate presented in the picture first along the horizontal lines, and next each obtained part along vertical lines then the cost of that breaking will be y_{1}+y_{2}+y_{3}+4*(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}).
Task
Write a program that for each test case:
 Reads the numbers x_{1}, x_{2}, ..., x_{m1} and y_{1}, y_{2}, ..., y_{n1}
 Computes the minimal cost of breaking the whole chocolate into single squares, writes the result.
Input
One integer in the first line, stating the number of test cases, followed by a blank line. There will be not more than 20 tests.
For each test case, at the first line there are two positive integers m and n separated by a single space, 2 <= m,n <= 1000. In the successive m1 lines there are numbers x_{1}, x_{2}, ..., x_{m1}, one per line, 1 <= x_{i} <= 1000. In the successive n1 lines there are numbers y_{1}, y_{2}, ..., y_{n1}, one per line, 1 <= y_{i} <= 1000.
The test cases will be separated by a single blank line.
Output
For each test case : write one integer  the minimal cost of breaking the whole chocolate into single squares.
Example
Input: 1 6 4 2 1 3 1 4 4 1 2 Output: 42
hide comments
mukulrajput34:
20240124 20:42:34
<snip>


deshiyan:
20220331 17:23:17
For all those PYTHON users, in the testcase loop have an extra input(), there is a blank space between every testcase. 

gamer4life:
20220115 20:26:16
@pallabtewarry just learn c++ 

pallabtewary:
20211102 04:29:22
One integer in the first line, stating the number of test cases, followed by a blank line


shubham2912:
20211003 09:42:05
For those getting NZEC in python be sure to take input of empty line in **each** test case 

iuc_01:
20210829 15:06:24
getting NZEC Runtime error in java


vikash_rishu92:
20210803 06:47:12
giving runtime error in python 

loser_404:
20210617 06:23:09
For above board optimal way to cut into square is:


myth_:
20210611 15:25:53
Make Sure to decrement the value of both m and n by 1...otherwise, it will give a segmentation error or a wrong answer 

ayushisriv:
20210610 17:23:58
why its showing runtime error for python 
Added by:  ThanhVy Hua 
Date:  20041223 
Time limit:  3s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  10th Polish Olympiad in Informatics, stage 1 