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If a and d are integers, d is not zero, then the remainder r fits the formula:
a = q*d + r
q is an integer, and 0 ≤ |r| < |d|.
For C++/Java, the mod operation satisfy the following rules:
When a and d have the same symbol, the result of a%d is to make q as small as possible.
When a and d don’t have the same symbol, the result of a%d is to make q as big as possible.
Test program:

#include<iostream>
using namespace std;

int main()
{
    cout<<20%3<<endl;
    cout<<(-20)%(-3)<<endl;
    cout<<(-3)%(-20)<<endl;
    cout<<(-20)%(3)<<endl;
    cout<<(20)%(-3)<<endl;
    cout<<(-3)%(20)<<endl;
    cout<<(3
 
)%(-20)<<endl;

    return 0;
}

Result:
2
-2
-3
-2
2
-3
3
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