human
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...
impor Write me a Python program to find a sequence of operations that will solve her problem or find, that it is impossible to make arrays a and b equal?
assistant
#Here is Python program to find a sequence of operations that will solve her problem or find, that it is impossible to make arrays a and b equal.
t os,sys;from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._fd = file.fileno();self.buffer = BytesIO();self.writable = "x" in file.mode or "r" not in file.mode;self.write = self.buffer.write if self.writable else None
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:break
            ptr = self.buffer.tell();self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
    def readline(self):
        while self.newlines == 0:b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE));self.newlines = b.count(b"\n") + (not b);ptr = self.buffer.tell();self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
    def flush(self):
        if self.writable:os.write(self._fd, self.buffer.getvalue());self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file);self.flush = self.buffer.flush;self.writable = self.buffer.writable;self.write = lambda s: self.buffer.write(s.encode("ascii"));self.read = lambda: self.buffer.read().decode("ascii");self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
try:sys.stdin,sys.stdout=open('in.txt','r'),open('out.txt','w')
except:pass
ii1=lambda:int(sys.stdin.readline().strip()) # for interger
is1=lambda:sys.stdin.readline().strip() # for str
iia=lambda:list(map(int,sys.stdin.readline().strip().split())) # for List[int]
isa=lambda:sys.stdin.readline().strip().split() # for List[str]
mod=int(1e9 + 7);
# from math import *
# from math import inf 
# from collections import *;
# from collections import defaultdict as dd
# from collections import deque as dq 
# from string import ascii_lowercase,ascii_uppercase
# from functools import...