C-Style Loops

You are given a C-style for loop:

for (variable = A; variable != B; variable += C)
  statement;

The loop initializes variable to A, then, while variable is not equal to B, repeatedly executes statement and increases variable by C. All arithmetic is performed on a $k$-bit unsigned integer type modulo $2^k$ (that is, within the range $0 \le x < 2^k$, taking remainders modulo $2^k$).

For the given $A$, $B$, $C$, and $k$, determine how many times statement is executed. If the loop never terminates, print FOREVER instead.

The input consists of several instances. Each instance is given on a single line containing four integers $A$, $B$, $C$, and $k$ separated by a single space. Here $k$ ($1 \le k \le 32$) is the number of bits of the loop control variable, and $A$, $B$, $C$ ($0 \le A, B, C < 2^k$) are the parameters of the loop.

The last line of the input contains four zeros; this line is not processed.

Print one line for each instance. The $i$-th line contains the number of times statement is executed in the $i$-th instance (a single integer), or FOREVER if the loop never terminates.