# Problem E

Recursion + Rand = !Fun

Consider the simple recursive function defined below. For a
particular parameter value, `i`, this
function might return several different values, depending on
the results of its calls to `myRNG()`.
That function returns random integer values in the range
$[0, 2^{31}-1]$, and you
should assume that it could return any sequence when called.
Your job is to tell the difference between values the function
`f(int i)` could produce and those it
could not.

int f(int i) { if (i <= 0) return 1; return a + myRNG() % b + f(i - 1 - (myRNG() % c)); }

## Input

Input contains up to $300$ test cases. Each test case is
described by five integer values, $a, b, c, i$, and $k$. The first four of these give the
values for the variables with the same names in the definition
of `f()`, while $k$ is the value you wish to know if
`f(i)` can return. Their limits are
$0 \le a \le 10$,
$1 \le b, c \le 10$,
$0 \le i \le 100$, and
$1 \le k \le 10\, 000$.
Input ends at the end of file.

## Output

For every test case, output the word “possible” if it’s
possible for `f(i)` to return the value
$k$, or “impossible” if
it’s not possible.

Sample Input 1 | Sample Output 1 |
---|---|

1 1 1 1 1 1 1 1 1 2 2 2 2 1 4 2 2 2 1 5 2 2 2 2 5 |
impossible possible possible impossible possible |