CF708B.Recover the String

普及/提高-

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题目描述

For each string ss consisting of characters '0' and '1' one can define four integers a00a_{00} , a01a_{01} , a10a_{10} and a11a_{11} , where axya_{xy} is the number of subsequences of length 22 of the string ss equal to the sequence x,y{x,y} .

In these problem you are given four integers a00a_{00} , a01a_{01} , a10a_{10} , a11a_{11} and have to find any non-empty string ss 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 10000001000000 .

输入格式

The only line of the input contains four non-negative integers a00a_{00} , a01a_{01} , a10a_{10} and a11a_{11} . Each of them doesn't exceed 10910^{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 10000001000000 .

输入输出样例

  • 输入#1

    1 2 3 4
    

    输出#1

    Impossible
    
  • 输入#2

    1 2 2 1
    

    输出#2

    0110
    
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