int result(int N, int R, int S, int E, int inverse)
{
    const int half = pow(2, N-1);

    // reached the base case
    if (N==0)
        return inverse;

    // if R is in the upper half
    else if (R < half)
    {
        if (E<half)         /*if the sum required is in the first quarter*/
            return result(N-1, R, S, E, inverse);
        if (S>=half)        /*if the sum required is in the second quarter*/
            return result(N-1, R, S-half, E-half, inverse);
        else                /*if the sum required is shared between the first and the second quarter*/
            return ( result(N-1, R, half-S-1, half-1, inverse)+result(N-1, R, half, E, inverse) );
    }

    // if R is in the lower half
    else
    {
        if (E<half)         /*if the sum required is in the third quarter*/
            return result(N-1, R-half, S, E, inverse);
        else if (S>=half)           /*if the sum required is in the fourth quarter*/
            return result(N-1, R-half, S-half, E-half, inverse*-1);
        else                /*if the sum required is shared between the third and the fourth quarter*/
            return ( result(N-1, R-half, half-S-1, half-1, inverse)+result(N-1, R-half, half, E, inverse*-1) );
    }
}