You will be given a point `(x,y)` relative to the center of the Ulam spiral (the point which represents one), and length `z`. The task is to check whether there exists a path from `(0,0)` to `(x,y)` of length `z`, assuming prime numbers are obstacles and each turn in path has an angle of 90 degrees. Path may not overlap with itself.

Examples of valid paths:
```
XXXX
   XX
    X
    X
    XXXXXXXX

    XXXXXX
XXXXX


XXXXXXXXXXXXXX
             X
             X
             X
             XXXXXXX
```

Examples of invalid paths:

```
XXXXXXXXXXXX
            XXXXX


XXXXX   XXXXXX
     X X
      X

XXX
   X
  X
   XXXXXXXXXXX

       X
       X
XXXXXXX!XXX
       X  X
       XXXX

The path above overlaps in a place marked with !.
```

For the record, this is a fragment of a Ulam spiral with `1 (0,0)` marked:

```
............#...#.......#...#
.#...#...........#.#.....#...
#.#.....#.#.....#.....#......
.........#...........#...#...
....#...#.......#.....#......
...#.........#...#.#...#.#.#.
......#.....#.........#.#...#
.#.....#...#.#...............
..............#.#.....#...#..
...#...#.#...#.......#...#.#.
..............#.#...#........
.....#...#.#.....#.#.#.....#.
#.#.#.#.#.#.#...#.......#....
.............#.#.#...........
........#...#.1##.#.#.#...#.#
.#.......#.#.#...............
..........#...#..............
...#.#...#.#...#...#.#...#...
..#...#...#.....#.....#.#...#
...........#...........#.....
......#.#.....#...#...#......
...#...#...........#.......#.
....#.....#...#.#............
.........#.#...#.....#...#...
#.#.#.........#.#.....#.....#
.#...#...........#.#.........
#.#.....#.....#...#.#........
.......#.........#.......#...
........#.#...#.#.........#..
```

## I/O examples
```
Input: (5, -1), 7 - true
Suggested path:
1##.#.#.#...#.#
XXXXXX.........
#..............

Input: (3, 0), 6 - true
Suggested path:
.#.#.#...........
#.1##X#.#.#...#.#
.#XXXX...........

Input: (-2, -1), 18 - true
Suggested path:
...#...#.#...#.......#...#.#.
..............#.#...#........
.....#...#.#.....#.#.#.....#.
#.#.#.#.#.#.#...#.......#....
.............#.#.#...........
........#...#.1##.#.#.#...#.#
.#.......#.#X#XX............
..........#.XX#XX............
...#.#...#.#.XX#XX.#.#...#...
..#...#...#...XX#X....#.#...#
...........#...XXX.....#.....

Input: (2, 1), 6 - false
Input: (-5, 2), 20 - true
Input: (-1, 0), 5 - false
```

## Additional considerations
`abs(x) <= 20` and `abs(y) <= 20` cases have to be resolved within the TIO time limit (soft bound; 60s) to verify validity of the answers.
The answers have to (theoretically and ideally) work on any reasonable input.