Disperse!

Every proper policeman's favourite sentence is "Citizens, disperse! There is nothing to see here!". That one sentence does not always settle the matter. Thick manuals explain what a policeman should do when citizens ignore a well meant warning and stay where they are. The most important piece of advice is to break the crowd up so that as few people as possible are left standing together. This task is about that kind of splitting. You have to find the different ways of splitting a crowd, so the policeman can pick whichever one is easiest to carry out.

To keep things simple we consider only "orthogonal standard crowds of evenly spread citizens", a term from Dispersing easily and quickly, by now a classic manual on the subject. A standard crowd is a square built from $N \times N$ square citizens with the same footprint. The policeman splits the crowd into two halves. The ideal halves have the same area and the same shape.

The way the two halves are kept apart matters too. The police have a special separating tape made for exactly this purpose, called a separator in police slang. The tape is quickly wound around a group of citizens to keep them away from everyone else. The tape is expensive, so it must never be cut or shortened, and the split has to leave each half with exactly the prescribed perimeter. The perimeter of a half is its whole outline, the part running along the edge of the square plus the part running along the cut.

Count the different ways of splitting a square standard crowd of side $N$ into two parts whose perimeter is exactly $M$. The two parts have to be the same, which means one can be laid onto the other using only translation, rotation and mirroring. So that no citizen gets hurt, the dividing line runs along the edges of the unit squares.

The first line contains a positive integer $Z$, the number of queries.

Each of the next $Z$ lines contains two integers $N$ and $M$ separated by a space. ($2 \le N \le 20$, $2 \le M \le 60$)

$N$ is the side of the square and $M$ is the length of the tape, that is the perimeter each half has to have after the split.

Print one line for each query.

If the crowd cannot be split into two identical parts of the given perimeter, print Rozdeleni neni mozne.

Otherwise print Existuje R ruznych moznosti., with R replaced by the number of different ways of splitting the crowd as prescribed. Two ways count as different when the resulting halves differ, that is when a half from one split cannot be laid onto a half from the other split by translation, rotation and mirroring.

Print both sentences exactly as written above, character for character.