CF1872C.Non-coprime Split

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, $\gcd(6, 9) = 3$ , $\gcd(8, 9) = 1$ , $\gcd(4, 2) = 2$ .

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 $l, r$ ( $1 \le l \le r \le 10^7$ ).

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.

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, $\gcd(14, 4) = 2$ .