Digit sum - MarisaOJ: Marisa Online Judge

An and Bình have a positive integer

$X$ and want to split it into the sum of two positive integers

$A$ and

$B$ . The true value of a positive integer is not in its magnitude but is determined by the sum of its digits. The two friends will be happy if

$A$ and

$B$ have equal digit sums. **Objective:** There are

$T$ test cases, each providing a positive integer

$X$ . For each test case, help An and Bình find two positive integers

$A$ and

$B$ such that they add up to

$X$ and have equal digit sums. ### Input - The first line contains an integer

$T$ (

$1 \leq T \leq 10000$ ); - Each of the following

$T$ lines contains a positive integer

$X$ (

$X \geq 2$ ). ### Output - For each test case, print any two positive integers

$A$ and

$B$ that satisfy the conditions on a single line. If no solution exists, print -1. ### Example Input:

$4 4 33 243 29$

Output:

$2 2 12 21 117 126 -1$

Let

$C(X)$ and

$S(X)$ denote the number of digits and the digit sum of the positive integer

$X$ . ### Subtasks - **Subtask 1 (20 points)**:

$X \leq 10000$ for all test cases. - **Subtask 2 (30 points)**: The total

$C(X)$ across all test cases does not exceed 1000. - **Subtask 3 (20 points)**: The total

$C(X)$ across all test cases does not exceed

$10^6$ and

$S(X)$ is even for all test cases. - **Subtask 4 (30 points)**: The total

$C(X)$ across all test cases does not exceed

$10^6$ .

Topic

Others

Rating

1500

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