{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eAlice and Bob decided to eat some fruit. In the kitchen they found a large bag of oranges and apples. Alice immediately took an orange for herself, Bob took an apple. To make the process of sharing the remaining fruit more fun, the friends decided to play a game. They put multiple cards and on each one they wrote a letter, either \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eA\u003c/span\u003e\u0027, or the letter \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eB\u003c/span\u003e\u0027. Then they began to remove the cards one by one from left to right, every time they removed a card with the letter \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eA\u003c/span\u003e\u0027, Alice gave Bob all the fruits she had at that moment and took out of the bag as many apples and as many oranges as she had before. Thus the number of oranges and apples Alice had, did not change. If the card had written letter \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eB\u003c/span\u003e\u0027, then Bob did the same, that is, he gave Alice all the fruit that he had, and took from the bag the same set of fruit. After the last card way removed, all the fruit in the bag were over.\u003c/p\u003e\u003cp\u003eYou know how many oranges and apples was in the bag at first. Your task is to find any sequence of cards that Alice and Bob could have played with.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains two integers, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e18\u003c/sup\u003e, \u003ci\u003exy\u003c/i\u003e \u0026gt; 1\u003c/span\u003e) — the number of oranges and apples that were initially in the bag.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint any sequence of cards that would meet the problem conditions as a \u003cspan class\u003d\"tex-font-style-it\"\u003ecompressed\u003c/span\u003e string of characters \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eA\u003c/span\u003e\u0027 and \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eB\u003c/span\u003e. That means that you need to replace the segments of identical consecutive characters by the number of repetitions of the characters and the actual character. For example, string \u003cspan class\u003d\"tex-font-style-tt\"\u003eAAABAABBB\u003c/span\u003e should be replaced by string \u003cspan class\u003d\"tex-font-style-tt\"\u003e3A1B2A3B\u003c/span\u003e, but cannot be replaced by \u003cspan class\u003d\"tex-font-style-tt\"\u003e2A1A1B2A3B\u003c/span\u003e or by \u003cspan class\u003d\"tex-font-style-tt\"\u003e3AB2A3B\u003c/span\u003e. See the samples for clarifications of the output format. The string that you print should consist of at most \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e6\u003c/sup\u003e\u003c/span\u003e characters. It is guaranteed that if the answer exists, its compressed representation exists, consisting of at most \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e6\u003c/sup\u003e\u003c/span\u003e characters. If there are several possible answers, you are allowed to print any of them.\u003c/p\u003e\u003cp\u003eIf the sequence of cards that meet the problem statement does not not exist, print a single word \u003cspan class\u003d\"tex-font-style-tt\"\u003eImpossible\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3B\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eImpossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1A1B\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first sample, if the row contained three cards with letter \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eB\u003c/span\u003e\u0027, then Bob should give one apple to Alice three times. So, in the end of the game Alice has one orange and three apples, and Bob has one apple, in total it is one orange and four apples.\u003c/p\u003e\u003cp\u003eIn second sample, there is no answer since one card is not enough for game to finish, and two cards will produce at least three apples or three oranges.\u003c/p\u003e\u003cp\u003eIn the third sample, cards contain letters \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003eAB\u003c/span\u003e\u0027, so after removing the first card Bob has one orange and one apple, and after removal of second card Alice has two oranges and one apple. So, in total it is three oranges and two apples.\u003c/p\u003e"}}]}