There is a cave of \(N\) cells where each cell has a trap or is safe to land. From a cell \(i\), you can jump to cells \(i+1\) or \(i+2\). Also, if number \(i\) is special, then you can also jump from cell \(i\) to cell \(i+A\) where \(A = number\; of\; primes\; in\; [1,i]\). A number \(i\) can be special if \(\frac{A}{i} \ge \frac{r1}{r2}\).

You are given the following:

Some arbitrary numbers \(r_1\) and \(r_2\)
The number of cells \(N\) in the cave where each cell contains either '#' or '*'
Details of the cave

Note: Here, '#' represents an empty cell and '*' means a trapped cell.

Your task is to determine the minimum number of steps that you have to walk to reach the \(N^{th}\) cell. Initially, you are at cell 1.

Input format

The first line contains an integer \(T\) denoting the number of test cases.
The first line of each test case contains two integers \(r_1\) and \(r_2\).
The second line of each test case contains an integer \(N\).
The third line contains a string of length \(N\) representing \(N\) cells where the first character of the string represents the first cell, second character represents the second cell, and so on. Each cell is either '#' or '*'.

Output format

For each test case, print the minimum number of steps that you have to walk to reach the \(N^{th}\) cell. Print the output in a separate line.

If it is not possible to reach the \(N^{th}\) cell, then print "\(No \; way!\)" without quotes.

Constraints

\(1 \le T \le 500\)

\(1 \le r_1, r_2 \le 10000\)

\(1 \le N \le 100000\)

Note: For large input files, use faster input methods.