Recall that a subsequence of a string is any string obtained by removing some subset of characters from the string, for instance "string", "sing", "i" and "sg" are all subsequences of "string". If the same subsequence can be obtained in exactly $$$t$$$ different ways, by removing different subsets of characters, we say that the subsequence occurs $$$t$$$ times.
Jingfei wants to create a nonempty bit string that has the following properties:
The input consists of a single line with four integers $$$a$$$, $$$b$$$, $$$c$$$, and $$$d$$$ ($$$0 \leq a,b,c,d \leq 10^9$$$).
Output a bit string that satisfies the given requirements. If there are several solutions, output any one of them. If there are no solutions, output "impossible".
3 4 2 1
01001
5 0 0 5
impossible