Hide
Problem D
Smallest Repetitive Multiple
We consider a number to be “repetitive” if it has an even number of digits (without leading zeros) and its first and second halves are equal (as strings). For example, the numbers $11$, $1367213672$, and $6060$ are repetitive, but $4$, $1230123$, and $121212$ are not.
Given an integer $x$, find its smallest multiple that is repetitive.
Input
The first line of the input contains a single integer $t$ ($1 \le t \le 10^5$) —the number of test cases. The description of the test cases follows.
Each test case consists of a single line with an integer $x$ ($1 \le x \le 10^8$).
Output
For each test case, output a single integer —the smallest multiple of $x$ that is repetitive. We can show that an answer always exists.
| Sample Input 1 | Sample Output 1 |
|---|---|
12 1 5 12 100 101 707 2431 12883 12341234 20987639 64705883 100000000 |
11 55 1212 100100 1010 1414 102102 991991 12341234 1111110311111103 58823535882353 100000000100000000 |
