Notice

Original Problem

Problem Statement

Snuke's factory has a Robot Arm EX with the following features.

• Robot Arm EX consists of $N$ arms and $N+1$ joints. The arms are numbered $1,2,\dots,N$ and the joints are numbered $0,1,\dots,N$. Arm $i$ connects joint $i-1$ and joint $i$.
• An angle and a length can be specified independently for each arm.
• Regarding the factory as a coordinate plane, the coordinates $(x_i,y_i)$ of joint $i$ are determined as follows.
• $(x_0,y_0) = (0,0)$
• Let $d_i$ be the length of arm $i$ and $\theta_{i}$ be the angle of arm $i$.
• With $\phi_{i} = \theta_{1} + \theta_{2} + \dots + \theta_{i}$, we have $(x_{i},y_{i})=(x_{i-1}+d_i\cos \phi_{i},y_{i-1}+d_i\sin \phi_{i})$
• The angle and length of each arm can be changed as follows.
• Change the angle of arm $i$ to $X$ degrees.
• Change the length of arm $i$ to $X$.

You are an engineer at Snuke's factory. You are given $Q$ queries in the following input format; process them.

• Query $0$: 0 i x: Change the angle of arm $i$ to $x$ degrees.
• Query $1$: 1 i x: Change the length of arm $i$ to $x$.
• Query $2$: 2 i: Print the $x$ coordinate and $y$ coordinate of joint $i$ on $1$ line, separated by a space.

Initially, all arms have an angle of $0$ degrees and a length of $1$.

AC has been confirmed with PyPy, but AC has not been confirmed with Python.

Constraints

• All input values are integers.
• $1 \le N \le 10^5$
• $1 \le Q \le 10^5$
• For queries $0,1,2$, $1 \le i \le N$
• For query $0$, $0 \le x < 360$
• For query $1$, $1 \le x \le 10$
• Query $2$ is given at least $1$ time.

Input

$N\ Q$
$query_1$
$query_2$
 $\vdots$
$query_Q$

Line $1$ contains $N,Q$ separated by a space.
Line $1 + i$ contains the $i$-th query, separated by spaces. See the problem statement for details.

Output

Let $q$ be the number of queries $2$. Print $q$ lines.
Line $i$ should contain the result of the $i$-th query $2$.
Print a newline at the end.

Your answer is considered correct if the absolute or relative error from the expected answer is at most $10^{-5}$.

Sample

Sample 1

Input

3 8
0 1 90
0 2 270
0 3 315
1 2 2
1 3 2
2 1
2 2
2 3

Output

0.000000 1.000000
2.000000 1.000000
3.414213 -0.414213

After the $5$ queries, Robot Arm EX takes the following shape.

The coordinates of joints $1,2,3$ are $(0,1),(2,1),(2+\sqrt 2,1-\sqrt 2)$, respectively.

1024 6
0 537 53
2 538
0 435 88
1 684 9
0 623 221
2 705

537.203630046 1.597271020
461.669761237 159.235272186