#12382Grid of Lamps

We have a grid of lamps. Some of the lamps are on, while others are off. The luminosity of a row/column is the number of its lighted lamps. You are given a permutation of the luminosities of the rows and a permutation of the columns’. Unfortunately, these values are not accurate but we know at least that they are not overestimates. You should tell us the minimum possible number of lighted lamps in this grid. As an example, consider the following grid. The lighted lamps are shown by 1’s and unlighted ones by 0’s. 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 The actual luminosities of the rows are < 3, 5, 2, 3, 1 >. A permutation of them could be < 1, 2, 5, 3, 3 >, and the inexact values you’d be given could be < 1, 1, 4, 2, 3 >.

Input

The first line of input contains an integer T ≤ 100 denoting the number of test-cases. Each test-case begins with two integers M and N , both in the interval [1, 1000], determining the number of rows and columns of the grid respectively. The next two lines give the luminosities, the first for rows (M values) and the second for columns (N values).

Output

For each test-case, on a single line, output the minimum conceivable number of lighted lamps.

3
2 2
2 0
0 2
1 4
2
1 0 1 1
2 4
3 1
0 2 1 2

3
3
5