Description

Once, a greedy king ordered his knight to build a wall outside his castle, requiring that the wall’s minimum distance from the castle must be at least $L$.

The castle is an $n$-gon. The king is extremely stingy and refuses to build even one extra meter of wall; if more is built, he will execute the knight in charge.

Please help this unlucky knight compute the minimal length of the wall that needs to be built.

Input Format

The first line contains two integers $n$, $L$, representing the number of sides of the polygon and the minimum distance.

Then follow $n$ lines. Each line contains two integers, the coordinates of a vertex on the polygon.

Output Format

Output a single integer: the minimal length of the wall, rounded to the nearest integer.

9 100
200 400
300 400
300 300
400 300
400 400
500 400
500 200
350 200
200 200

1628

Hint

Constraints

• For $100\%$ of the testdata, it is guaranteed that $3\le n\le1000$, $1\le L\le1000$, and $-10^4\leq x_i,y_i\leq 10^4$.

Translated by ChatGPT 5