Group Photos - Repovive Starter Round 9 | Repovive

25A. Group Photos

500 pts1s256 MB

A group of $n$ friends want to take group photos, but they do not have a tripod.

For each photo, one friend takes the photo, and all the other $n-1$ friends appear in it. The photographer does not appear in that photo.

Each friend wants to appear in at least $k$ photos. What is the minimum number of photos they need to take?

Constraints

$2 \le n \le 1000$
$1 \le k \le 1000$

Input

n \quad k

Output

\mathrm{answer}

Samples

Input

2 3

Explanation

Each photo contains only one friend. They can take three photos of each other, for a total of six. Fewer photos cannot give both friends three appearances.

Output

Input

3 2

Explanation

Each friend can take one photo. Then every friend appears in the other two photos. Two photos would give only four appearances in total, but six are needed.

Output

Input

4 4

Explanation

Number the friends from 1 to 4. They can choose friends 1, 2, 3, 4, 1, and 2 as the photographers, in that order. Friends 1 and 2 appear in four photos each, and friends 3 and 4 appear in five photos each. Five photos would give only fifteen appearances in total, but sixteen are needed.

Output

A group of $n$ friends want to take group photos, but they do not have a tripod.

For each photo, one friend takes the photo, and all the other $n-1$ friends appear in it. The photographer does not appear in that photo.

Each friend wants to appear in at least $k$ photos. What is the minimum number of photos they need to take?

$2 \le n \le 1000$
$1 \le k \le 1000$

n \quad k

\mathrm{answer}

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25A. Group Photos

Constraints

Input

Output

Samples

25A. Group Photos

Constraints

Input

Output

Samples