For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy 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 a00, a01, a10, a11 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.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
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.
Examples
Input
Copy
Output
Copy
Input
Copy
Output
Copy
首先从a00和a11可以求出0和1的数量;
假设目前为0000...001111..;
显然a01=num0*num1,a10=0;
那么我们移动一个1去左边,a10++,a01--;但总数还是不变;
那么合理的解必须是a10+a01=num0*num1;
值得注意的是:当00或11=0时,0或1可能有1个也可能没有;
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EPFL - Fighting