### C Looooops

Time Limit: 1000 ms
Memory Limit: 65536 KiB

#### Problem Description

A Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; variable += C) statement;

I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repeats statement followed by increasing the variable by C. We want to know how many times does the statement get executed for particular values of A, B and C, assuming that all arithmetics is calculated in a k-bit unsigned integer type (with values 0 <= x < 2

I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repeats statement followed by increasing the variable by C. We want to know how many times does the statement get executed for particular values of A, B and C, assuming that all arithmetics is calculated in a k-bit unsigned integer type (with values 0 <= x < 2

^{k}) modulo 2^{k}.#### Input

The input consists of several instances. Each instance is described by a single line with four integers A, B, C, k separated by a single space. The integer k (1 <= k <= 32) is the number of bits of the control variable of the loop and A, B, C (0 <= A, B, C < 2

The input is finished by a line containing four zeros.

^{k}) are the parameters of the loop.The input is finished by a line containing four zeros.

#### Output

The output consists of several lines corresponding to the instances on the input. The i-th line contains either the number of executions of the statement in the i-th instance (a single integer number) or the word FOREVER if the loop does not terminate.

#### Sample Input

3 3 2 16 3 7 2 16 7 3 2 16 3 4 2 16 0 0 0 0

#### Sample Output

0 2 32766 FOREVER

#### Hint

poj2115 有链接提示的题目请先去链接处提交程序，AC后提交到SDUTOJ中，以便查询存档。

#### Source

CTU Open 2004