There is a special multiplication operator such that Table of special multiplication operation Thus ab = b, ba = c, bc = a, cb = c, ... For example, you are given the string bbbba and the character a, (b(bb))(ba) = (bb)(ba) [as bb = b] = b(ba) = bc = a [as bb = b] [as ba = c] [as bc = a] By adding suitable brackets, bbbba can produce a according to the above multiplication table. You are asked to write a program to show the morphing steps of a string into an expected character, or otherwise, output ‘None exist!’ if the given string cannot be morphed as expected. Input The first line of the input file gives the number of test cases. Each case consists of two lines. The first line is the starting string which has at most 100 characters. The second line is the target character. All characters in the input are within the range of a-c. Output For each test case, your output should consist several lines, showing the morphing steps of a string into the character. In case there are more than one solution, always try to start the morphing from the left. Print a blank line between consecutive sets of output. Sample Input 2 bbbba a bbbba a

2/2 Sample Output bbbba bbba bba bc a bbbba bbba bba bc a