Super calculator#2250

Super calculator

1 second

64 megabytes

Easy

Super calculator performs only a single arithmetic operation — multiplication of natural numbers. The upper boundary for the range of representable natural numbers in the calculator is unknown; let us denote this boundary by $P$ . If the result of multiplication $a \cdot b$ a \cdot b is greater than or equal to $P$ ( $a \cdot b \geq P$ a \cdot b \geq P, where $a$ and $b$ are the factors), two scenarios are possible:

The answer is $(a \cdot b) mod P$ (a \cdot b) \bmod P.
The answer is a random number from the range of valid values (calculator malfunction).

Given the values of the factors ( $a$ , $b$ ) and the result ( $c$ ), write a program to analyze the calculator's behavior. The output must be a single number determined as follows:

$0$ , if $c = a \cdot b$ c = a \cdot b;
$1$ , if a malfunction occurred;
the minimal value of $P$ .

Input

The input is a string containing the numbers $a$ , $b$ , and $c$ , separated by spaces. $a$ and $b$ are the factors, $c$ is the result.

Output

The output is a single number.

Note: The length of the input string does not exceed $15$ .

Examples

Example 1

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a \cdot b

a \cdot b \geq P

(a \cdot b) mod P

c = a \cdot b