Circle and Many Triangles

Input

The input is given from Standard Input in the following format:

$N \ K$

Output

• Please output the $K$-th triangle area.
• Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{−9}$.

Constraints

• $3 \le N \le 200,000$
• $1 \le K \le \frac{N(N-1)(N-2)}{6}$

Subtasks

Subtask 1 [ $160$ points ]

• $N \le 100$

Subtask 2 [ $240$ points ]

• $N \le 1000$

Subtask 3 [ $450$ points ]

• $N \le 200,000$

Output

• Please output the $K$-th triangle area.
• Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{−9}$.

Constraints

• $3 \le N \le 200,000$
• $1 \le K \le \frac{N(N-1)(N-2)}{6}$

Subtasks

Subtask 1 [ $160$ points ]

• $N \le 100$

Subtask 2 [ $240$ points ]

• $N \le 1000$

Subtask 3 [ $450$ points ]

• $N \le 200,000$

Input

The input is given from Standard Input in the following format:

$N \ K$

Examples

Input

4 3

Output

1.0000000000000

Input

6 9

Output

0.86602540378

Input

12 220

Output

1.29903810568

inputFormat

Input

The input is given from Standard Input in the following format:

$N \ K$

outputFormat

Output

• Please output the $K$-th triangle area.
• Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{−9}$.

Constraints

• $3 \le N \le 200,000$
• $1 \le K \le \frac{N(N-1)(N-2)}{6}$

Subtasks

Subtask 1 [ $160$ points ]

• $N \le 100$

Subtask 2 [ $240$ points ]

• $N \le 1000$

Subtask 3 [ $450$ points ]

• $N \le 200,000$

Output

• Please output the $K$-th triangle area.
• Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{−9}$.

Constraints

• $3 \le N \le 200,000$
• $1 \le K \le \frac{N(N-1)(N-2)}{6}$

Subtasks

Subtask 1 [ $160$ points ]

• $N \le 100$

Subtask 2 [ $240$ points ]

• $N \le 1000$

Subtask 3 [ $450$ points ]

• $N \le 200,000$

Input

The input is given from Standard Input in the following format:

$N \ K$

Examples

Input

4 3

Output

1.0000000000000

Input

6 9

Output

0.86602540378

Input

12 220

Output

1.29903810568

样例

4 3

1.0000000000000