P4317 Huashen's Number Theory Problem

As is well known, for many years Huashen has crushed various OJ, OI, CF, TC ... of course including CH.

One day, Huashen came to give another lecture. As usual, there was a super hard problem afterwards... We weaklings suffered again. The problem is as follows: Let $\text{sum}(i)$ denote the number of $1$ s in the binary representation of $i$. Given a positive integer $N$, Huashen asks you to compute $\prod_{i=1}^{N}\text{sum}(i)$, that is, the product of $\text{sum}(1)\sim\text{sum}(N)$.

A positive integer $N$.

One integer: the answer modulo $10000007$.

Constraints: For $100\%$ of the testdata, $1 \le N \le 10^{15}$. Translated by ChatGPT 5