The pipe-weed of Shire is famous for its befuddling effect.
But you don't know probably that hobbits use it to educate their
offsprings. They roll pipe-weed into sticks and let children play with them.
A child may even study arithmetics if the parents make digits and
signs of operations using such sticks. The plus sign is obtained
by putting a stick over another stick crosswise and the sign of equality
is two parallel sticks. The picture shows how to make
digits from 0 to 9 using pipe-weed sticks.
Little hobbits spend half of their education
time to learn the addition, so we couldn't obtain information about how to
make other signs of operations.
Sam once told that as a child he had liked to make fun of his father by
moving sticks in an equality in such a way that it had become
invalid. And now Sam invented a new entertainment for his own
children. He arranges sticks on a table so that they make up an
arithmetic equality of the form
X + Y = Z
and asks the children to make it valid by moving no more than K sticks.
Each of the numbers X, Y and Z must have less than 9 digits and must not have any leading zeroes (but it can be equal to zero). It is forbidden to change the number of signs and digits
as well as throw out sticks or add new sticks. Help Sam to determine
if his problem can be solved.
The first line contains an expression of the form
a1 + a2 = b
(0 ≤ a1, a2, b < 108). The second line contains the integer K (0 ≤ K ≤ 100).
If it is possible to make the expression valid by moving no more than
K sticks, then output one of the valid expressions that can be obtained this way.
Otherwise, output «Impossible».
Problem Author: Sergey Pupyrev
Problem Source: VIII USU Open Personal Contest (March 3, 2007)