Description

Construct a Numeral Triangle according to the following rules. You will be given three positive integers: $s$, a starting number; $d$, a delta (the amount by which to increase each number in the triangle); and $r$ the number of rows.

1. The first row contains the number $s$.
2. Each of the next rows has one more number than the previous row.
3. Each number in the triangle is $d$ more than the previous number in the triangle.
4. Before putting a number in the triangle, it is transformed to a single digit. That is, if the number is more than one digit, replace it by the sum of the digits, repeating until the sum is one digit (for example, $1938 \Rightarrow 21 \Rightarrow 3$).

Here are two examples of Numeral Triangles:

start=2, delta=3, rows=5

2
5 8
2 5 8
2 5 8 2
5 8 2 5 8

start=221, delta=2, rows=4

5
7 9
2 4 6
8 1 3 5

Input Format

There are 5 lines of data. Each line has 3 positive integers, $s$, $d$, and $r$. The numbers are separated by spaces and each is less than 100,000.

Output Format

For each line of data, print the sum of all numbers on the $r$th line of the Numeral Triangle.

Explanation

Example 1: Input 2 3 5

• The numbers on row 5 are 5, 8, 2, 5, 8.
• Sum = $5+8+2+5+8 = 28$.

Example 2: Input 221 2 4

• $s = 221 \Rightarrow 2+2+1=5$. $d=2$.
• The numbers on row 4 are 8, 1, 3, 5.
• Sum = $8+1+3+5 = 17$.

2 3 5

28

221 2 4

17

184 231 35

140

71 5 27

135

1 24 100

397