| ## Page 1 | |
| 10193 | |
| All You Need Is Love | |
| ”All you need is love. All you need is love. | |
| All you need is love, love... love is all you need.” | |
| The Beatles | |
| There was invented a new powerfull gadget by the International Beautifull Machines corporation | |
| called the love machine! Given a string made of binary digits, the love machine answers if it’s made | |
| only of love, that is, if all you need is love to build that string. The definition of love for the love | |
| machine is another string of binary digits, given by a human operator. Let’s say we have a string L | |
| which represents “love” and we give a string S for the love machine. We say that all you need is love | |
| to build S, if we can repeatly subtract L from S until we reach L. The subtraction defined here is the | |
| same arithmetic subtraction in base 2. By this definition it’s easy to see that if L > S (in binary), then | |
| S is not made of love. | |
| If S = L then S is obvious made of love. | |
| Let’s see an example. Supose S = “11011” and L = “11”. If we reapetly subtract L from S, we | |
| get: 11011, 11000, 10101, 10010, 1111, 1100, 1001, 110, 11. So, given this L, all you need is love to | |
| build S. Because of some limitations of the love machine, there can be no string with leading zeroes. | |
| That is, “0010101”, “01110101”, “011111”, etc. are invalid strings. Strings which have only one digit | |
| are also invalid (it’s another limitation). | |
| Your task in this problem is: given two valid binary strings, S1 and S2, find if it’s possible to have a | |
| valid string L such that both S1 and S2 can be made only of L (i.e. given two valid strings S1 and S2, | |
| find if there exists at least one valid string L such as both S1 and S2 are made only of L). For instance, | |
| for S1 = 11011 and S2 = 11000, we can have L = 11 such that S1 and S2 are both made only of L (as | |
| we can see in the example above). | |
| Input | |
| The first line of input is a positive integer N < 10000 which stands for the number of teste cases. Then, | |
| 2 ∗N lines will follow. Each pair of lines consists in one teste case. Each line of the pair stands for each | |
| string (S1 and S2) to be entered as an input for the love machine. No string will have more than 30 | |
| characters. You can assume that all strings in the input will be valid acording to the rules above. | |
| Output | |
| For each string pair, you must print one of the following messages: | |
| Pair #p: All you need is love! | |
| Pair #p: Love is not all you need! | |
| Where p stands for the pair number (starting from 1). You should print the first message if there | |
| exists at least one valid string L such as both S1 and S2 can be made only of L. Otherwise, print the | |
| second line. | |
| ## Page 2 | |
| Sample Input | |
| 5 | |
| 11011 | |
| 11000 | |
| 11011 | |
| 11001 | |
| 111111 | |
| 100 | |
| 1000000000 | |
| 110 | |
| 1010 | |
| 100 | |
| Sample Output | |
| Pair #1: All you need is love! | |
| Pair #2: Love is not all you need! | |
| Pair #3: Love is not all you need! | |
| Pair #4: All you need is love! | |
| Pair #5: All you need is love! |