# 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 2k for some integer k (0 <= k <=7):

1. Consider the 8-bit binary representation of the numbers A and B, and name them A' and B' respectively.
2. Compute C = A' + B' in base 10 (i.e. 1+1=2). Assume c1c2c3c4c5c6c7 be the sequence of digits in C.
3. Since the addition is done in base 10, there may be some digit ci = 2. For such a digit, change ci to 0, and add 1 to ci-1 and ci+1. In case i = 0, only add 1 to ci+1. You may assume that the input numbers are small enough that this case never happens for i = 7.
4. 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 = 2k 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.

```23 2
7 1
64 16
0 0
```

## Sample Output

```29
11
80
```
Submit

Source: Tehran, Asia Region - Regional 2011