Problem Description

Xiao Lan wants to construct a digit string of length $10000$ with the following requirements:

1. Xiao Lan does not like the digit $0$, so the digit string must not contain $0$.

2. Xiao Lan likes the digits $3$ and $7$, so the digit string must contain both $3$ and $7$.

How many digit strings satisfy the requirements? This number can be very large; you only need to output the result modulo $10^9 + 7$.

Output Format

Output one integer in one line, representing the answer.

Hint

Translated by ChatGPT 5