AIM Tech Round 3 (Div. 1) |
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constructive algorithms

greedy

implementation

math

*1900

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B. Recover the String

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFor 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.

Input

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}.

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

1 2 3 4

Output

Impossible

Input

1 2 2 1

Output

0110

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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