Linear Interpolation

Version: Phuoc Hung OJ Extended

Problem Statement

Given endpoints $a$, $b$ and a parameter $t\in[0,1]$, compute their linear interpolation $y=a+(b-a)t$. The value equals $a$ at $t=0$ and $b$ at $t=1$. Print $y$ with exactly 6 digits after the decimal point.

Input

The only line contains real endpoints $a$, $b$ followed by parameter $t$.

Output

Print interpolated value $y$ with exactly 6 decimal places.

Subtasks

• Subtask 1 (100 points): $a,b,t$ are finite; $0\le t\le1$.

Examples

Example 1

Input

0 10 0.25

Output

2.500000

Explanation. The endpoint difference is 10. Evaluating 0 + (10 - 0) × 0.25 = 2.5 and formatting gives 2.500000.

Example 2

Input

5 9 0.5

Output

7.000000

Explanation. The endpoint difference is 4. Evaluating 5 + (9 - 5) × 0.5 = 7 and formatting gives 7.000000.

Example 3

Input

-10 10 0.75

Output

5.000000

Explanation. The endpoint difference is 20. Evaluating -10 + (10 - -10) × 0.75 = 5 and formatting gives 5.000000.