1 s   64 MB

## Description

Adding binary numbers is a very simple task, and very similar to the longhand addition of decimal numbers. As with decimal numbers, you start by adding the bits (digits) one column at a time, from right to left. Unlike decimal addition, there is little to memorize in the way of rules for the addition of binary bits:

0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11

Just as with decimal addition, when the sum in one column is a two-bit (two-digit) number, the least significant figure is written as part of the total sum and the most significant figure is “carried” to the next left column. Consider the following examples:

11 1 <-- Carry bits --> 1 11 1001101 1001001 1000111 + 0010010 + 0011001 + 1010110 -------- --------- --------- 1011111 1100010 10011101

The addition problem on the left did not require any bits to be carried, since the sum of bits in each column was either 1 or 0, not 10 or 11. In the other two problems, there definitely were bits to be carried, but the process of addition is still quite simple.

## Input

The first line of input contains an integer N, (1 ≤ N ≤ 1000), which is the number of binary addition problems that follow. Each problem appears on a single line containing two binary values separated by a single space character. The maximum length of each binary value is 80 bits (binary digits). Note: The maximum length result could be 81 bits (binary digits).

## Output

For each binary addition problem, print the problem number, a space, and the binary result of the addition. Extra leading zeroes must be omitted.

### Sample Output

3
1001101 10010
1001001 11001
1000111 1010110
1 1011111
2 1100010
3 10011101

## Source

Greater New York 2005