Hi! I am interested in evaluating this expression:

where $$$\text{popcount}(i)$$$ is the number of 1 digits in the binary expansion of $$$i$$$.

Or, in C++:

int mod = 1e9 + 7;
for (int i = 1; i <= n; ++i){
        // avoid calculating popcount more than once
        g = popcount(i);
        sum += a * a * g * g;
        sum %= mod;
    }
cout << sum;

The problem is that $$$N$$$ is very large ($$$10^{16}$$$). I am completely stuck, so thanks for your help!