# Two-Way Carry Propagation

Time Limit: 1 Second Memory Limit: 32768 KB

In 1897, the mathematician L. Aguile invented a special operation (#) over the binary representation of integer numbers.

In its simple form, *A#B* is computed according to the following steps, where *A* is a non-negative integer number and *B*
is of the form 2^{k} for some integer *k* (0 <= *k* <=7):

- Consider the 8-bit binary representation of the numbers
*A*and*B*, and name them*A'*and*B'*respectively. - Compute
*C*=*A'*+*B'*in base 10 (i.e. 1+1=2). Assume*c*be the sequence of digits in_{1}c_{2}c_{3}c_{4}c_{5}c_{6}c_{7}*C*. - Since the addition is done in base 10, there may be some digit
*c*= 2. For such a digit, change_{i}*c*to 0, and add 1 to_{i}*c*and_{i-1}*c*. In case_{i+1}*i*= 0, only add 1 to*c*. You may assume that the input numbers are small enough that this case never happens for_{i+1}*i*= 7. - The step 3 is repeated until there is no digit 2 in
*C*, which is finally considered as the binary representation of*A#B*.

For example, if

*A* = 23 (binary 00010111), and *B* = 2 (binary 00000010), then the following sequence of numbers
defines the value of *C* in successive stages of the above algorithm: 00010121 -> 00010202 -> 00010210 -> 00011020
-> 00011101 which is the number 29.
The problem is to input *A* and *B*, and output *A#B*. All numbers are in expressed in base 10 and you must take care of
the conversions to binary and vice versa.

## Input

The input consists of several test cases. Each test case comes on a separate line containing two integer numbers *A* and
*B*, separated by blanks, where *A* is between 0 and 255, and *B* = 2^{k} for some 0 <= *k* <=7. You may assume that at every step during the computation of *A#B* as defined above, *C* fits in an 8-bit number. You may assume that there are no blank characters at the beginning or at the end of the lines. The input terminates with a single line containing two zero which should not be processed.

## Output

For each test case, output a single line containing the number *A#B* in decimal.

## Sample Input

23 2 7 1 64 16 0 0

## Sample Output

29 11 80Submit

Source: Tehran, Asia Region - Regional 2011