Recover the String

题意翻译

以下$4$个参数： $a_{00}$表示$01$串中$00$对的数量 $a_{01}$表示$01$串中$01$对的数量 $a_{10}$表示$01$串中$10$对的数量 $a_{11}$表示$01$串中$11$对的数量 比如：$01010$中， $a_{00}=3$ 、 $a_{01}=3$ 、 $a_{10}=3$ 、 $a_{11}=1$ 输出$4$个参量严格等于给定参量的$01$串，如果不能输出"$Impossible$". 翻译$by$ @Happynewyear

题目描述

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 $ .

输入输出格式

输入格式

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} $ .

输出格式

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 $ .

输入输出样例

输入样例 #1

1 2 3 4

输出样例 #1

Impossible

输入样例 #2

1 2 2 1

输出样例 #2

0110