Alice is feeling bored while sitting on the riverbank with her sister, when she notices a 2D White Rabbit with a 2D pocket watch run past. She follows it down a rabbit hole when suddenly she falls a long way to a curious 2D plane.

In this 2D plane she discovered she can only move using a sequence of movements. Those movements are limited to:

Scaling, denoted as $S_{c}$ (where ${c}$ is a nonzero rational number). If Alice is currently at $(x,y)$, then $S_{c}$ takes her to $(cx,cy)$.
Translation, denoted as $T_{a,b}$ (where ${a}$ and ${b}$ are rational numbers). If Alice is currently at $(x,y)$, then $T_{a,b}$ takes her to $(a+x,b+y)$.
Rotation, denoted as $R_{a,b}$ (where ${a}$ and ${b}$ are rational numbers and $a^2+b^2=1$). If Alice is currently at $(x,y)$, then $R_{a,b}$ takes her to $(ax+by,ay-bx)$. In other words, $R_{a,b}$ is a clockwise rotation about the origin, at an angle $\theta$ where $\text{cos}\theta=a$ and $\sin\theta=b$.
Flip X-axis, denoted as $\mathbf{F}_{X}$. If Alice is currently at $(x,y)$, then $\mathbf{F}_{X}$ takes her to $(x,-y)$.
Flip Y-axis, denoted as $\mathbf{F}_{Y}$. If Alice is currently at $(x,y)$, then $\mathbf{F}_{Y}$ takes her to $(-x,y)$.
Inversion, denoted as ${I}$ (more precisely, inversion in the unit circle). If Alice is currently at $(x,y)$, then ${I}$ takes her to $\left(\frac{x}{x^2+y^2},\frac{y}{x^2+y^2}\right)$.

Also, Alice discovered that when she is at $(0,0)$ before she performs an inversion, she is taken to a special place called Wonderland. In Wonderland, performing any of the other movements (scaling, translation, rotation or flip) will return her to Wonderland, and performing an inversion moves her back to $(0,0)$.

Now, Alice has a sequence of $N$ such movements to make. Moreover, she performs this sequence of $N$ movements a total of ${K}$ times. Your task is to determine her final location after her adventure.

If Alice's final location is $(x_f,y_f)$, it's easy to see that $x_f$ and $y_f$ are rational. Let $x_f=A/B$ and $y_f=C/D$ (both in lowest terms). Understandably, ${A}$, ${B}$, ${C}$ and ${D}$ can be really large integers, so instead of asking for $x_f$ and $y_f$ we will only ask for the values $AB^{-1}\:\text{mod}\:(10^9+7)$ and $CD^{-1}\:\text{mod}\:(10^9+7)$.

Input Format

The first input contains a single integer, ${T}$, which is the number of test cases. The next lines contain the descriptions of the ${T}$ test cases.

The first line of each test case contains four values $N$, ${K}$, $x_s$ and $y_s$. $N$ and ${K}$ are integers (described above), and $(x_s,y_s)$ is the initial location of Alice ($x_s$ and $y_s$ are rational numbers).

The next $N$ lines each contains the description of a movement in the sequence, which is one of the following:

S c, which denotes scaling (${c}$ is a nonzero rational number),
T a b, which denotes translation (${a}$ and ${b}$ are rational numbers),
R a b, which denotes rotation (${a}$ and ${b}$ are rational numbers and $a^2+b^2=1$),
F X, which denotes flip X-axis,
F Y, which denotes flip Y-axis, and
I, which denotes inversion.

Output Format

If Alice's final location is Wonderland, output WONDERLAND.

If Alice's final location is $(x_f,y_f)$, and $x_f=A/B$ and $y_f=C/D$ in irreducible form, then output the two integers $AB^{-1}\:\text{mod}\:(10^9+7)$ and $CD^{-1}\:\text{mod}\:(10^9+7)$ in a line separated by a single space. However, if either ${B}$ or ${D}$ is not invertible, also output WONDERLAND.

Constraints

$1\leq T\leq10^5$

$1\leq N\leq10^5$

The sum of the $N$'s in a single test file is $\leq10^5$

$1\leq K\leq10^{15}$

Each rational number is expressed in irreducible form $A/B$ with the following constraints:

$-10^9<A<10^9$

$1\leq B<10^9$

Sample Input

2
3 2 0/1 0/1
T -2/1 3/1
R 3/5 4/5
I
5 1 2/1 -2/1
F X
S 3/2
T -3/1 -3/1
I
F Y

Sample Output

881896558 492241383
WONDERLAND

Explanation

In the first test case, $(x_s,y_s)=(0,0)$, $K=2$ and the sequence of operations is $[T_{-2,3},R_{3/5,4/5},I]$.

$\begin{array}{ccccc}T_{-2,3}:&\text{(0,0)}&\to&\text{(-2,3)}\\ R_{3/5,4,5}:&\text{(-2,3)}&\to&\text{(6/5,17/5)}\\ I:&\text{(6/5,17/5)}&\to&\text{(6/65,17/65)}\\ T_{-2,3}:&\text{(6/65,17/65)}&\to&\text{(-124/65,22/65)}\\ R_{3/5,4,5}:&\text{(-124/65,212/165)}&\to&\text{(476/325,1132/325)}\\ I:&\text{(476/325,1132/325)}&\to&\text{(119/1160,2831160)}\\ \end{array}$

Therefore, the final location is $(x_f,y_f)=(119/1160,283/1160)$. So we print:

$119\cdot1160^{-1}\:\text{mod}\:(10^9+7)=881896558$ and:

$283\cdot1160^{-1}\:\text{mod}\:(10^9+7)=492241383$.

In the second test case, $(x_s,y_s)=(2,-2)$, $K=1$ and the sequence of operations is $[F_X,S_{3/2},T_{-3,-3},I,F_Y]$.

$\begin{aligned}F_X\colon&(2,-2)&\to&(2,2)\ S_{3/2}\colon&(2,2)&\to&(3,3)\ T_{-3,-3}\colon&(3,3)&\to&(0,0)\ I\colon&(0,0)&\to&\text{Wonderland}\F_Y\colon&
\text{Wonderland}&\to&\text{Wonderland}\end{aligned}$

Therefore, the final location is Wonderland.

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