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- Project Euler #129: Repunit divisibility

# Project Euler #129: Repunit divisibility

# Project Euler #129: Repunit divisibility

_{This problem is a programming version of Problem 129 from projecteuler.net}

A number consisting entirely of ones is called a repunit. We shall define to be a repunit of length ; for example, .

Given that is a positive integer and , it can be shown that there always exists a value, , for which is divisible by , and let be the least such value of ; for example, and .

The least value of for which first exceeds ten is .

Given , compute .

**Input Format**

The first line of input contains , the number of test cases.

Each test case consists of a single line containing single integer, .

**Constraints**

*Test files #1-2:*

*Test files #3-6:*

**Output Format**

For each test case, output a single line containing a single integer, .

**Sample Input**

```
2
7
41
```

**Sample Output**

```
6
5
```

**Explanation**

As mentioned in the problem statement, and .