Bodyguard Arrangement in Matrix

You are given a matrix with n rows and m columns. Each cell in the matrix can either have a bodyguard (represented by 1) or be empty (represented by 0). For each row and each column, a target number of bodyguards is specified. Your task is to determine whether there exists a placement of bodyguards such that every row i has exactly r_i bodyguards and every column j has exactly c_j bodyguards.

A necessary condition is that the total number of bodyguards in rows equals that in columns, i.e.,

$\sum_{i=1}^{n}r_i=\sum_{j=1}^{m}c_j$

Moreover, by the Gale-Ryser theorem, a sufficient and necessary condition for the existence of such a binary matrix is that for every k from 1 to n,

$\sum_{i=1}^{k}r_i \leq \sum_{j=1}^{m}\min(c_j,k)$

If both conditions hold, output YES; otherwise, output NO.

inputFormat

The first line contains an integer T (T ≥ 3) representing the number of test cases.

Each test case is described as follows:

• The first line contains two integers n and m, denoting the number of rows and columns, respectively.
• The second line contains n integers: r1, r2, ..., rn, representing the required number of bodyguards for each row.
• The third line contains m integers: c1, c2, ..., cm, representing the required number of bodyguards for each column.

Input numbers are separated by spaces.

outputFormat

For each test case, output a single line containing YES if there exists a valid arrangement of bodyguards under the given constraints; otherwise, output NO.

sample

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

YES
YES
NO