C. Non-coprime Split
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two integers $$$l \le r$$$. You need to find positive integers $$$a$$$ and $$$b$$$ such that the following conditions are simultaneously satisfied:

  • $$$l \le a + b \le r$$$
  • $$$\gcd(a, b) \neq 1$$$

or report that they do not exist.

$$$\gcd(a, b)$$$ denotes the greatest common divisor of numbers $$$a$$$ and $$$b$$$. For example, $$$\gcd(6, 9) = 3$$$, $$$\gcd(8, 9) = 1$$$, $$$\gcd(4, 2) = 2$$$.

Input

The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases.

Then the descriptions of the test cases follow.

The only line of the description of each test case contains $$$2$$$ integers $$$l, r$$$ ($$$1 \le l \le r \le 10^7$$$).

Output

For each test case, output the integers $$$a, b$$$ that satisfy all the conditions on a separate line. If there is no answer, instead output a single number $$$-1$$$.

If there are multiple answers, you can output any of them.

Example
Input
11
11 15
1 3
18 19
41 43
777 777
8000000 10000000
2000 2023
1791791 1791791
1 4
2 3
9840769 9840769
Output
6 9
-1
14 4
36 6
111 666
4000000 5000000 
2009 7
-1
2 2
-1
6274 9834495
Note

In the first test case, $$$11 \le 6 + 9 \le 15$$$, $$$\gcd(6, 9) = 3$$$, and all conditions are satisfied. Note that this is not the only possible answer, for example, $$$\{4, 10\}, \{5, 10\}, \{6, 6\}$$$ are also valid answers for this test case.

In the second test case, the only pairs $$$\{a, b\}$$$ that satisfy the condition $$$1 \le a + b \le 3$$$ are $$$\{1, 1\}, \{1, 2\}, \{2, 1\}$$$, but in each of these pairs $$$\gcd(a, b)$$$ equals $$$1$$$, so there is no answer.

In the third sample test, $$$\gcd(14, 4) = 2$$$.