Divisors and Multiples

We have $4 \times 3 = 12$.

From this equation we can observe the following facts.

• $3$ is a divisor of $12$, and $12$ is a multiple of $3$.
• $4$ is a divisor of $12$, and $12$ is a multiple of $4$.

Given two numbers, write a program that determines which of the following three relationships holds between the first number and the second number.

1. The first number is a divisor of the second number.
2. The first number is a multiple of the second number.
3. The first number is neither a divisor nor a multiple of the second number.

The input consists of several test cases. Each test case is given on one line as two natural numbers, each not exceeding $10{,}000$. The two numbers are never equal. The last line of the input contains two zeros, and this line is not processed.

For each test case, print factor if the first number is a divisor of the second number, multiple if the first number is a multiple of the second number, or neither if it is neither, each on its own line.