Sequences

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Summary

For each query with a first term, non-zero common difference, and value, print the term index if the value is in the arithmetic sequence, otherwise X.

Level: Easy3 of 10
Topics: Math, Implementation, Number theory
Solved: No attempts yet

Problem

An arithmetic sequence is a sequence of numbers in which every term after the first is obtained by adding a fixed number, called the common difference, to the previous term.

For example, $3, 5, 7, 9$ is an arithmetic sequence whose first term is $3$ and whose common difference is $2$ : each term after the first is formed by adding $2$ to the previous one. Here $3$ is term $1$ and $9$ is term $4$ .

Given a first term, a common difference, and a value, determine whether the value can appear in the sequence. If it can, output which term it is; otherwise output the letter X.

Input

The input consists of several lines. Each line contains three integers separated by spaces:

the first term of the sequence,
the common difference (a non-zero integer),
the value to test.

The input is terminated by a line containing 0 0 0, which must not be processed.

Output

For each input line except the terminating line, print a single line containing the term number of the value, or X if the value is not part of the sequence.

Constraints

The first term, the common difference, and the value are each between $-6000000$ and $6000000$ .

Hint

For the first query 3 2 11, the sequence is $3, 5, 7, 9, 11, \dots$ , so $11$ is term $5$ .

For the second query -1 -3 -8, the sequence is $-1, -4, -7, -10, \dots$ , so $-8$ does not appear and the answer is X.

Examples3

Example 1
Input
```
3 2 11
-1 -3 -8
0 0 0
```
Expected output
```
5
X
```
Example 2
Input
```
3 2 3
0 0 0
```
Expected output
```
1
```
Example 3
Input
```
3 2 1
0 0 0
```
Expected output
```
X
```