#47Medium

Splitting a segment into equal parts

Time: 1 s · Memory: 256 MB

Loops

Statement

A segment $[a, b]$ is given on the number line. It is split into $n$ equal parts. Find the length $h$ of a part and the division points: $a, a + h, a + 2h, \ldots, b$ — $n + 1$ points in total.

Input format

A single line with three integers $a$ , $b$ , $n$ ( $-100 \le a < b \le 100$ , $1 \le n \le 50$ ).

Output format

The first line contains $h$ . The second line contains the $n + 1$ points from left to right. All numbers with exactly 2 digits after the decimal point.

Examples

Input

1 3 5

Output

0.40
1.00 1.40 1.80 2.20 2.60 3.00

Input

0 10 4

Output

2.50
0.00 2.50 5.00 7.50 10.00

Note

$h = \dfrac{b - a}{n}$ and the $i$ -th point is $a + i \cdot h$ . It is better to compute each point with $a + i \cdot h$ : with x += h the small floating-point errors pile up on every step.

Splitting a segment into equal parts

Time: 1 s · Memory: 256 MB

Loops

Statement

A segment $[a, b]$ is given on the number line. It is split into $n$ equal parts. Find the length $h$ of a part and the division points: $a, a + h, a + 2h, \ldots, b$ — $n + 1$ points in total.

Input format

A single line with three integers $a$ , $b$ , $n$ ( $-100 \le a < b \le 100$ , $1 \le n \le 50$ ).

Output format

The first line contains $h$ . The second line contains the $n + 1$ points from left to right. All numbers with exactly 2 digits after the decimal point.

Examples

Input

1 3 5

Output

0.40
1.00 1.40 1.80 2.20 2.60 3.00

Input

0 10 4

Output

2.50
0.00 2.50 5.00 7.50 10.00

Note

$h = \dfrac{b - a}{n}$ and the $i$ -th point is $a + i \cdot h$ . It is better to compute each point with $a + i \cdot h$ : with x += h the small floating-point errors pile up on every step.