1546_A. 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.
```python
cases=int(input())
for idx in range(cases):
    n=int(input())
    a=list(map(int, input().split()))
    b=list(map(int, input().split()))
    if sum(a)!=sum(b): print(-1)
    elif a==b: print(0)
    else:
        tuples=[]
        count=0
        for i in range(n):
            if a[i]==b[i]: continue
            if a[i]>b[i]:
                while a[i]>b[i]:
                    diff1=a[i]-b[i]
                    for j in range(n):
                        if i==j: continue
                        if a[j]<b[j]:
                            diff2=b[j]-a[j]
                            diffmin=min(diff1,diff2)
                            a[i]-=diffmin
                            a[j]+=diffmin
                            diff1-=diffmin
                            count+=diffmin
                            for k in range(diffmin): tuples.append((i+1,j+1))
        print(count)
        for i,j in tuples:
            print(i,j)
```