Write a predicate modulo/3 that calculates the modulo of two Peano numbers.

In the system of the Peano numbers, \(0\) is presented by 0, \(1\) by s(1), \(2\) by s(s(0)), and so on. To be precise, \(n\) is represented by taking 0 and wrapping it \(n\) times with s/1.

The following predicates are assumed to be defined.

• p_add(A,B,C) iff \(A + B = C\)
• p_sub(A,B,C) iff \(A - B = C\)
• p_mul(A,B,C) iff \(A \cdot B = C\) (The version in Dodona allows you to use it to divide, does your implementation do that? Why?)
• p_exp(A,B,C) iff \(A^B = C\)
• less_strict(X,Y): X is strictly less than Y
• greater_strict/2: X is strictly larger than Y
• less_or_eq(X,Y): X is less or equal to Y
• greater_or_eq/2: X is larger or equal to Y

This exercise can be solved with and without using recursion. Try them both.