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 1 000 000.

对于每个仅由字符 '0' 和 '1' 组成的字符串 $s$，可以定义四个整数 $a_{00}$、$a_{01}$、$a_{10}$ 和 $a_{11}$，其中 $a_{xy}$ 表示字符串 $s$ 中长度为 2 的子序列中等于序列 $\{x,\,y\}$ 的个数。

本题中，你将被给定四个整数 $a_{00}$、$a_{01}$、$a_{10}$、$a_{11}$，要求找出任意一个满足这些值的非空字符串 $s$，或判定不存在这样的字符串。可以证明：若至少存在一个解，则必存在一个长度不超过 $1\,000\,000$ 的解。

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 109.

输入仅包含一行，其中有四个非负整数 $a_{00}$、$a_{01}$、$a_{10}$ 和 $a_{11}$。每个数均不超过 $10^9$。

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 1 000 000.

如果存在一个非空字符串，能够匹配输入中的四个整数，则在输出的唯一一行中打印该字符串；否则，打印“Impossible”。你的答案长度不得超过 $1\,000\,000$。