You have an n × n chessboard and k rooks. Rows of this chessboard are numbered by integers from 1 to n from top to bottom and columns of this chessboard are numbered by integers from 1 to n from left to right. The cell (x, y) is the cell on the intersection of row x and collumn y for 1 ≤ x ≤ n and 1 ≤ y ≤ n.
The arrangement of rooks on this board is called good , if no rook is beaten by another rook.
A rook beats all the rooks that shares the same row or collumn with it.
The good arrangement of rooks on this board is called not stable , if it is possible to move one rook to the adjacent cell so arrangement becomes not good. Otherwise, the good arrangement is stable . Here, adjacent cells are the cells that share a side .
Please, find any stable arrangement of k rooks on the n × n chessboard or report that there is no such arrangement.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.The first line of each test case contains two integers n, k (1 ≤ k ≤ n ≤ 40) — the size of the chessboard and the number of rooks.
Output
If there is a stable arrangement of k rooks on the n × n chessboard, output n lines of symbols . and R. The j-th symbol of the i-th line should be equals R if and only if there is a rook on the cell (i, j) in your arrangement.If there are multiple solutions, you may output any of them.If there is no stable arrangement, output -1.
Examples
Note
In the first test case, you should find stable arrangement of 2 rooks on the 3 × 3 chessboard. Placing them in cells (3, 1) and (1, 3) gives stable arrangement.In the second test case it can be shown that it is impossbile to place 3 rooks on the 3 × 3 chessboard to get stable arrangement.