A10497. 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 $1000000$ .