19131번 - Huge Products 다국어

Bobo has a lot of integers. Frankly, he has $a_1$ number of $1$, $a_2$ number of $2$, $\dots$, $a_{10}$ number of $10$.

Today, bobo would like to pick some of the numbers and calculate their product (If none of the numbers are chosen, the product is defined as $1$).  bobo is curious about the number of different products he can obtain, modulo $(10^9 + 7)$.

$10$ integers $a_1, a_2, \dots, a_{10}$ ($0 \leq a_i \leq 10^9$).

A single integer denotes the number of products.