Junior analyst

We have to put the ball in the hole in minimum movement of the tiles.

You are given a starting position for a rat which is stuck in a maze at an initial point (0, 0) (the maze can be thought of as a 2-dimensional plane). The maze would be given in the form of a square matrix of order 'N' * 'N' where the cells with value 0 represent the maze’s blocked locations while value 1 is the open/available path that the rat can take to reach its destination. The rat's destination is at ('N' - 1, 'N' - 1). Your task is to find all the possible paths that the rat can take to reach from source to destination in the maze. The possible directions that it can take to move in the maze are 'U'(up) i.e. (x, y - 1) , 'D'(down) i.e. (x, y + 1) , 'L' (left) i.e. (x - 1, y), 'R' (right) i.e. (x + 1, y).

Note:

Here, sorted paths mean that the expected output should be in alphabetical order.

For Example:

Given a square matrix of size 4*4 (i.e. here 'N' = 4):
1 0 0 0
1 1 0 0
1 1 0 0
0 1 1 1 
Expected Output:
DDRDRR DRDDRR 
i.e. Path-1: DDRDRR and Path-2: DRDDRR

The rat can reach the destination at (3, 3) from (0, 0) by two paths, i.e. DRDDRR and DDRDRR when printed in sorted order, we get DDRDRR DRDDRR.

Yogesh is a very intelligent student and is interested in research in Machine Learning domain. His college has only one professor, Mr. Peter working in that field. He approaches the professor for the same, but professor wants to test him first.

To pass the test Yogesh must answer Q questions correctly. In all the Q questions, professor gives him three positive integers : A, B and K where A ≤ B.

Now Yogesh has to find an integer P such that it is closest to integer A and there are at least K prime numbers in range [A, P], where A <= P <= B.

Help Yogesh to find and print minimum possible P or print -1 if there no such possible integer.

Note: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.