B. Recover the String

хугацааны хязгаарлалт 1 секунд

санах ойн хязгаарлалт 256 мегабайт

оролт стандарт оролт

гаралт стандарт гаралт

For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.

In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.


The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.


If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.

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