Nice Pairs

Two natural numbers $n$ and $m$ form a nice pair when the following holds.

• Cutting some digits off the back of $n$ and placing them, in the same order, in front of what is left gives $m$.

For example, cutting $345$ off the back of $12345$ and placing it in front gives $34512$, so $(12345, 34512)$ is a nice pair.

You are given two natural numbers $A$ and $B$ with the same number of digits. Count the pairs $(x, y)$ with $A \le x < y \le B$ such that $(x, y)$ is a nice pair.

Two different cut lengths can produce the same $m$. In that case the pair $(x, y)$ is counted once.

The first line contains two natural numbers $A$ and $B$ separated by a space. $1 \le A \le B \le 2{,}000{,}000$, and $A$ and $B$ have the same number of digits.

Print the number of nice pairs as a single integer.