Rockdu is a pony living in Ponyville. His best friend, Macaronlin, also lives there. Rockdu values friendship so much that he shares everything with Macaronlin, even integers.

Here comes the question: how to share an integer with someone else? For an integer $$$x$$$, Rockdu splits it into two parts. Specifically, he treats $$$x$$$ in decimal form as a string without leading zeros, and splits it into two non-empty substrings at a certain position. He then considers these two substrings as two separate decimal integers, denoted as $$$x_1$$$ (the former) and $$$x_2$$$ (the latter).

Rockdu wants $$$x_1$$$ and $$$x_2$$$ to be as close in value as possible. Therefore, among all possible splits, he chooses the one that minimizes the absolute difference between $$$x_1$$$ and $$$x_2$$$. For example, if $$$x = 1003$$$, there are three possible ways to split it: $$$1|003$$$, $$$10|03$$$, and $$$100|3$$$. Rockdu chooses the first way because it yields the smallest absolute difference: $$$|1 - 3| = 2$$$, whereas the other ways give $$$|10 - 3| = 7$$$ and $$$|100 - 3| = 97$$$.

Let $$$f(x)$$$ be defined as the smallest absolute difference between the two integers resulting from splitting $$$x$$$. For example, $$$f(1003)=2$$$. Given two integers $$$l$$$ and $$$r$$$, Rockdu wants to calculate the sum of $$$f(i)$$$ for all $$$i$$$ in the range $$$[l, r]$$$. Since the answer may be very large, please output it modulo $$$10^9 + 7$$$.