There is a monster who is destroying planet Earth. To counter them, there is a special force of heroes. The heroes are numbered according to their strengths. The strength of the $k$-th hero is the $k$-th largest number in the set

$S = \{ x \ | \ x = \sum_{i = 1}^{20} \frac{a_i}{6^i}, \ 0 \leq a_i \leq 5 \ \text{for each} \ 1 \leq i \leq 20\}.$

Find the strength of the hero who is weaker than $553453543$ heroes.

Let $M = 10^9 + 7$. It can be shown that the answer can be expressed as an irreducible fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \not\equiv 0 \pmod{M}$.

Output the integer equal to $p \cdot q^{-1} \mod M$. In other words, output such an integer $x$ that $0 \leq x < M$ and $x \cdot q \equiv p \pmod{M}$.