Divisors and Multiples

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Summary

For each pair of numbers, print factor if the first divides the second, multiple if the first is a multiple of the second, or neither.

Level: Easy1 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

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.

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

Input

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.

Output

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.

Examples1

Example 1

Input

Expected output

factor
multiple
neither