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## 문제

Geek Challenge [SKRZAT] is an old, old game from Poland that uses a game console with two buttons plus a joy stick. As is true to its name, the game communicates in binary, so that one button represents a zero and the other a one. Even more true to its name, the game chooses to communicate so that the base of the number system is minus two, not plus two, so we’ll call this representation “Weird Binary”. Thus the bit positions label the powers of minus two, as seen in the following five-bit tables:

 Bits Value Bits Value Bits Value Bits Value 00000 0 01000 -8 10000 16 11000 8 00001 1 01001 -7 10001 17 11001 9 00010 -2 01010 -10 10010 14 11010 6 00011 -1 01011 -9 10011 15 11011 7 00100 4 01100 -4 10100 20 111100 12 00101 5 01101 -3 10101 21 11101 13 00110 2 01110 -6 10110 18 11110 10 00111 3 01111 -5 10111 19 11111 11

 Bits Value Bits Value Bits Value Bits Value 01010 -10 00010 -2 11010 6 10010 14 01011 -9 00011 -1 11011 7 10011 15 01000 -8 00000 0 11000 8 10000 16 01001 -7 00001 1 11001 9 10001 17 01110 -6 00110 2 11110 10 10110 18 01111 -5 00111 3 11111 11 10111 19 01100 -4 00100 4 11100 12 10100 20 01101 -3 00101 5 11101 13 10101 21

Numbers are presented on the screen in Weird Binary, and then numbers are accepted in response from the console as a stream of zeroes and ones, terminated by a five-second pause.

You are writing a computer program to support the novice geek in playing the game by translating numbers between decimal and Weird Binary.

## 입력

The first line in the file gives the number of problems being posed without any white space. Following are that many lines. Each line will either be a conversion into Weird Binary or out of Weird Binary: the letter "b" indicates that the rest of the line is written in Weird Binary and needs to be converted to decimal; the letter "d" indicates that the rest of the line is written in decimal and needs to be converted to Weird Binary.

The input data are in the range to fit within a 15-bit Weird Binary number, which represents the decimal number range –10922 to 21845, inclusive.

## 출력

For each conversion problem, show the type of problem, its input string, and the converted result in the format shown below, replicating even the spacing exactly as shown. Leading zeroes are not allowed.

## 예제 입력

10
b 1001101
b 0111111
b 101001000100001
b 010010001000010
b 100110100110100
d -137
d 137
d 8191
d -10000
d 21000


## 예제 출력

From binary: 1001101 is 61
From binary: 0111111 is -21
From binary: 101001000100001 is 19937
From binary: 010010001000010 is -7106
From binary: 100110100110100 is 15604
From decimal: -137 is 10001011
From decimal: 137 is 110011001
From decimal: 8191 is 110000000000011
From decimal: -10000 is 10100100110000
From decimal: 21000 is 101011000011000