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## HS11LFSR - Linear Feedback Shift Register

Given a Fibonacci linear feedback shift register (LFSR) please emulate its behaviour.

### Input

First t<100, the number of test cases. In each of the following t lines:
1<l<=1024 - the length of the register (the number of bits),
seed - the initial value of the LFSR in binary format,
0<p<l - the number of taps (bits which influence the input),
p1,p2,...,pp - the taps in increasing order in decimal format, 0<pi<=l.

### Output

Please output, byte by byte, the first 128 output bits of the register in hexadecimal format.

### Example

```Input:
2
3 010 2 2 3
5 00110 3 1 3 5

Output:
A7 D3 E9 74 3A 9D 4E A7 D3 E9 74 3A 9D 4E A7 D3
85 9B C2 4D E1 A6 70 53 B8 29 DC 14 6E 0A 37 85
```

### Scoring

By solving this problem you score 10 points.

 Added by: kuszi Date: 2012-01-19 Time limit: 0.306s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM32-GCC ASM64 GAWK MAWK BC C-CLANG CPP14 CPP14-CLANG COBOL COFFEE D-CLANG D-DMD DART ELIXIR FANTOM FORTH GOSU GRV JS-MONKEY KTLN NIM NODEJS OBJC OBJC-CLANG OCT PICO PROLOG PYPY PY_NBC R RACKET RUST CHICKEN SED SQLITE SWIFT UNLAMBDA VB.NET Resource: High School Programming League