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...
Using python3 can you solve the prior task?
 Write me a Python code 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 code to find a sequence of operations that will solve her problem or find, that it is impossible to make arrays a and b equal.

from __future__ import division, print_function
from math import sqrt,gcd,ceil,floor,log,factorial
from itertools import permutations,combinations
from collections import Counter, defaultdict
from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
import os,sys,math
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip

def ii():  return int(input())
def si():  return input()
def mi():  return map(int,input().split())
def msi(): return map(str,input().split())
def li():  return list(mi())

def add_set():
    sys.setrecursionlimit(1000000)
    threading.stack_size(1024000)
    thread = threading.Thread(target=main)
    thread.start()

mod=1000000007

def ncr(n,r): 
    return factorial(n)//(factorial(r)*factorial(max(n-r,1)))
    
def isPower2(x): 
    return (x and (not(x&(x-1))))
    
def isPrime(n): 
    if (n <= 1) : return False
    if (n <= 3) : return True
    if (n % 2 == 0 or n % 3 == 0) : return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True

def solve():
    t=ii()
    for _ in range(t):
        n=ii()
        #n,m=mi()
        a=li()
        b=li()
        dec,inc=0,0
        ine,de=[],[]
        
        for i in range(n):
            if a[i]>b[i]:
                dec+=a[i]-b[i]
                de+=[i+1]*(a[i]-b[i])
                
            elif a[i]<b[i]:
                inc+=b[i]-a[i]
                ine+=[i+1]*(b[i]-a[i])
                
        if inc==dec:
            print(inc)
            for j in range(inc):
                print(de[j],ine[j])
            
        else:
            print(-1)
    


BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
       ...