Problem I
Sine Wave

Let us attempt to draw a sine wave using whitespace and the X character. Sine waves are usually drawn horizontally, but standard program output is ordered from top to bottom. We will therefore draw our wave vertically.

Our program shall accept two arguments:

• $N$, which controls how many waves should be drawn

• $L$, which controls how many lines are used to print the waves

Most programming languages have a built in function to compute the sine of a value. For example, Python has a built in math.sin function that we could leverage. Alas, the sine function takes radians, distance travelled along the perimeter of a unit circle, as input. How will we figure out the value to input for each line?

A circle is $2\pi$ radians. Since we wish to draw $N$ waves, the total distance in radians is given by $2\pi N$. Therefore, the distance travelled from one line to the next will be $\frac{2\pi N}{L}$. We can then see that for the $i$th line, where $0\le i<L$, the distance travelled in radians up to that line is $r_i=i\cdot \frac{2\pi N}{L}$.

We are not done yet, as $\sin (x)$ will return a real number between $-1.0$ and $1.0$, inclusive. We cannot print a negative number of Xs, and to make sure the wave is clearly visible, we still need an appropriate number of Xs. Let us use $40$ for the full width, or peak-to-peak amplitude, of the waves. In other words, an amplitude of $20$, also called semi-amplitude. Then we need to linearly transform the return value of the sine function to a real number between $0$ and $40$, and round that number to figure out how many X characters to print. See the table below for examples.

Input

Input consists of two lines. The first line contains the integer $N$, the number of waves to draw, where $1\le N\le 10$. The second line contains the integer $L$, the number of lines used to draw the waves, where $1\le L\le 1000$.

Output

Draw the sine wave as described above. Exactly one newline character (\n) should immediately follow the last X on each line. If your program outputs additional whitespace, it will be considered incorrect.

1
20

XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXX
XXXX
X

X
XXXX
XXXXXXXX
XXXXXXXXXXXXXX

2
12

XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXX
XXX
XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXX
XXX

1
40

XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXX
XXXXXX
XXXX
XX
X



X
XX
XXXX
XXXXXX
XXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX