AquaMoon and Two Arrays

AquaMoon and Cirno are playing an interesting game with arrays. Cirno has prepared two arrays a and b, both consist of n non-negative integers. AquaMoon can perform the following operation an arbitrary number of times (possibly zero):

• She chooses two indices i and j (1 ≤ i, j ≤ n), then decreases the i-th element of array a by 1, and increases the j-th element of array a by 1. The resulting values at i-th and j-th index of array a are a_i - 1 and a_j + 1, respectively. Each element of array a must be non-negative after each operation. If i = j this operation doesn't change the array a.

AquaMoon wants to make some operations to make arrays a and b equal. Two arrays a and b are considered equal if and only if a_i = b_i for all 1 ≤ i ≤ n.

Help AquaMoon to find a sequence of operations that will solve her problem or find, that it is impossible to make arrays a and b equal.

Please note, that you don't have to minimize the number of operations.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100).

The second line of each test case contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 100). The sum of all a_i does not exceed 100.

The third line of each test case contains n integers b_1, b_2, ..., b_n (0 ≤ b_i ≤ 100). The sum of all b_i does not exceed 100.

Output

For each test case print "-1" on the only line if it is impossible to make two arrays equal with some sequence of operations.

Otherwise, print an integer m (0 ≤ m ≤ 100) in the first line — the number of operations. Then print m lines, each line consists of two integers i and j — the indices you choose for the operation.

It can be proven that if it is possible to make two arrays equal with some sequence of operations, there exists a sequence with m ≤ 100.

If there are multiple possible solutions, you can print any.

Example

Input

4 4 1 2 3 4 3 1 2 4 2 1 3 2 1 1 0 0 5 4 3 2 1 0 0 1 2 3 4

Output

2 2 1 3 1 -1 0 6 1 4 1 4 1 5 1 5 2 5 2 5

Note

In the first example, we do the following operations:

• i = 2, j = 1: [1, 2, 3, 4] → [2, 1, 3, 4];
• i = 3, j = 1: [2, 1, 3, 4] → [3, 1, 2, 4];

In the second example, it's impossible to make two arrays equal.

inputFormat

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100).

The second line of each test case contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 100). The sum of all a_i does not exceed 100.

The third line of each test case contains n integers b_1, b_2, ..., b_n (0 ≤ b_i ≤ 100). The sum of all b_i does not exceed 100.

outputFormat

Output

For each test case print "-1" on the only line if it is impossible to make two arrays equal with some sequence of operations.

Otherwise, print an integer m (0 ≤ m ≤ 100) in the first line — the number of operations. Then print m lines, each line consists of two integers i and j — the indices you choose for the operation.

It can be proven that if it is possible to make two arrays equal with some sequence of operations, there exists a sequence with m ≤ 100.

If there are multiple possible solutions, you can print any.

Example

Input

4 4 1 2 3 4 3 1 2 4 2 1 3 2 1 1 0 0 5 4 3 2 1 0 0 1 2 3 4

Output

2 2 1 3 1 -1 0 6 1 4 1 4 1 5 1 5 2 5 2 5

Note

In the first example, we do the following operations:

• i = 2, j = 1: [1, 2, 3, 4] → [2, 1, 3, 4];
• i = 3, j = 1: [2, 1, 3, 4] → [3, 1, 2, 4];

In the second example, it's impossible to make two arrays equal.

样例

4
4
1 2 3 4
3 1 2 4
2
1 3
2 1
1
0
0
5
4 3 2 1 0
0 1 2 3 4

2
2 1
3 1
-1
0
6
1 4
1 4
1 5
1 5
2 5
2 5

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