CF708B Recover the String

For each string $ s $ consisting of characters '0' and '1' one can define four integers $ a_{00} $ , $ a_{01} $ , $ a_{10} $ and $ a_{11} $ , where $ a_{xy} $ 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 $ a_{00} $ , $ a_{01} $ , $ a_{10} $ , $ a_{11} $ 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 $ 1000000 $ .

The only line of the input contains four non-negative integers $ a_{00} $ , $ a_{01} $ , $ a_{10} $ and $ a_{11} $ . Each of them doesn't exceed $ 10^{9} $ .

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 $ 1000000 $ .