G - 222

Score : $600$ points

Problem Statement

We have a sequence $2,22,222,2222,\ldots$, where the $i$-th term is an $i$-digit integer whose digits are all $2$.

Where does a multiple of $K$ appear in this sequence for the first time? If the first multiple of $K$ is the $x$-th term of the sequence, print $x$; if there is no multiple of $K$, print -1.

Given $T$ cases, solve each of them.

Constraints

• $1 \leq T \leq 200$
• $1 \leq K \leq 10^8$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$T$

$\text{case}_1$

$\text{case}_2$

$\vdots$

$\text{case}_T$

Each case is in the following format:

Output

Print $T$ lines. The $i$-th line should contain the answer for $\text{case}_i$.

4
1
7
10
999983

1
6
-1
999982

We have four cases.

• $2$ is a multiple of $1$.
• None of $2,22,222,2222,22222$ is a multiple of $7$, but $222222$ is.
• None of $2,22,\ldots$ is a multiple of $10$.