Recover the String

1000ms

262144K

Description:

For each string s consisting of characters '0' and '1' one can define four integers a₀₀, a₀₁, a₁₀ and a₁₁, 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 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.

Sample Input:

1 2 3 4

Sample Output:

Impossible

Sample Input:

1 2 2 1

Sample Output:

Informação

Provedor Codeforces

Código CF708B