As you know, a complex number is often represented as the sum of a real part and an imaginary part. is such an example, where is the real part, is the imaginary part, and is the imaginary unit.
Given a prime number and a positive integer , your program for this problem should output the product of all the complex numbers satisfying the following conditions.
Both the real part and the imaginary part are non-negative integers less than or equal to .
At least one of the real part and the imaginary part is not a multiple of .
For instance, when and , the complex numbers satisfying the conditions are (), (), and (), and the product of these numbers, that is, is .
输入格式
The input consists of a single test case of the following format.
is a prime number less than . is a positive integer less than or equal to .
输出格式
Output two integers separated by a space in a line. When the product of all the complex numbers satisfying the given conditions is , the first and the second integers should be and , respectively. Here, means the integer between and , inclusive, such that is divisible by .
As exemplified in the main section, when and , the product to be calculated is . However, since , and are displayed in Sample Output 1.
