Reyno has invented his own encryption algorithm (called Reyno's Super Algorithm), which he uses to encrypt messages he sends to his friends. His algorithm works as follows:

- He writes down his message. If it has an odd length, he adds a space to the end.
- He breaks his message into pairs of characters, forming pairs in total.
- He converts each pair into a number by multiplying the ASCII value of the first character by and adding the value of the second character.
- He generates pseudo-random numbers .
- He multiplies the value of the first pair by and outputs the result modulo (which is prime).
- He repeats step for the second, third, fourth, etc. pair until he encrypts the entire message.

To generate the random numbers, he uses a linear congruential generator (which you have seen before). His generator uses the function:

Which means that to generate the random number (), he multiplies the number () by modulo . For the first number (), also known as the seed value, he picks a random number that he really likes. Reyno thinks his algorithm is unbreakable. Can you prove him wrong?

#### Input Specification

The first line of the input provides the number of test cases, . test cases follow. Each test case begins with the integer . The next line contains integers, the encrypted values of the message.

For of the cases, Reyno picks a seed value less than or equal to and only uses uppercase letters and spaces.

#### Output Specification

For each test case, output the original message. If there are multiple solutions, output the one with the smallest seed value.

#### Sample Input

```
3
6
9285 14187 23117 13153 39535 12859
19
11055 2553 29781 23952 11741 3298 15519 1333 12875 23540 747 19405 34018 37512 25977 36696 20201 2481 20533
9
35534 39644 22348 34428 2726 25535 33105 3555 6320
```

#### Sample Output

```
HELLO WORLD
THIS IS REYNO'S UNBREAKABLE ALGORITHM
FOUR MILK NO SUGAR
```

#### Explanation for Sample

In the first test case, Reyno uses a seed value of , which means the encryption works as follows:

Value | Original Pair (Value) | Encrypted Value |
---|---|---|

1 | `HE` (9285) |
9285 |

1997 | `LL` (9804) |
14187 |

27118 | `O` (10144) |
23117 |

22469 | `WO` (11215) |
13153 |

20504 | `RL` (10572) |
39535 |

17281 | `D` (8736) |
12859 |

## Comments