You are given two arrays of integers: $$$a_1, a_2, \ldots, a_n$$$ and $$$b_1, b_2, \ldots, b_m$$$.

You need to determine if it is possible to transform array $$$a$$$ into array $$$b$$$ using the following operation several (possibly, zero) times.

Among all non-empty subarrays$$$^{\text{∗}}$$$ of $$$a$$$, choose any with the maximum sum, and replace this subarray with an arbitrary non-empty integer array.

If it is possible, you need to construct any possible sequence of operations. Constraint: in your answer, the sum of the lengths of the arrays used as replacements must not exceed $$$n + m$$$ across all operations. The numbers must not exceed $$$10^9$$$ in absolute value.

$$$^{\text{∗}}$$$An array $$$a$$$ is a subarray of an array $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n, m$$$ ($$$1 \le n, m \le 500$$$) — the lengths of arrays $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^6 \le a_i \le 10^6$$$) — the elements of array $$$a$$$.

The third line of each test case contains $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ ($$$-10^6 \le b_i \le 10^6$$$) — the elements of array $$$b$$$.

It is guaranteed that the sum of the values of $$$n$$$ across all test cases does not exceed $$$500$$$.

It is guaranteed that the sum of the values of $$$m$$$ across all test cases does not exceed $$$500$$$.

Output

For each test case, output $$$-1$$$ if it is impossible to transform array $$$a$$$ into array $$$b$$$.

Otherwise, in the first line, output the number of operations $$$0 \leq q \leq n + m$$$. Then output the operations in the following format in the order they are performed.

In the first line of each operation, print three numbers $$$l, r, k$$$ ($$$1 \leq l \leq r \leq |a|$$$). In the second line, print $$$k$$$ integers $$$c_1 \ldots c_k$$$, which means replacing the segment $$$a_l, \ldots, a_r$$$ with the array $$$c_1, \ldots, c_k$$$.

The sum of $$$k$$$ across all $$$q$$$ operations must not exceed $$$n + m$$$. Additionally, it must hold that $$$-10^9 \leq c_i \leq 10^9$$$.

You do not need to minimize the number of operations.

Note

In the first test, the initial array is modified as follows:

$$$$$$ [2, -3, 2, 0] \to [2, -3, -3] \to [-3, -3, -3] \to [-3, -7, -3] \to [-3, -7, 0] $$$$$$

You may choose to output empty lines or not. Empty lines in the example are added for convenience.

Curse

Examples