Cute Numbers

Given two integers l and r, count the number of cute numbers in the range [l, r]. A number is called cute if it contains a palindrome substring of length at least 2. In other words, if the decimal representation of a number contains either two consecutive identical digits or a pattern where a digit repeats after one intervening digit, then the number is cute.

Formally, let the digits of a number be denoted by \(d_0, d_1, d_2, \dots, d_{n-1}\). The number is cute if there exists an index i such that either

\(d_i = d_{i+1}\)

or

\(d_i = d_{i+2}\)

For example, the number 101 is cute because although its adjacent digits are not identical, it forms a palindrome (\(1\ 0\ 1\)); the number 110 is cute because it contains the adjacent palindrome 11; however, 102 and 1201 are not cute.

Since the answer might be very large, output it modulo \(10^9+7\).

inputFormat

The input consists of two space‐separated integers l and r.

outputFormat

Output a single integer, the count of cute numbers between l and r (inclusive) modulo \(10^9+7\).

sample

100 110

3