Problem

A positive integer is a palindrome if its decimal representation (without leading zeros) is a palindromic string (a string that reads the same forwards and backwards). For example, the numbers 5, 77, 363, 4884, 11111, 12121 and 349943 are palindromes. A range of integers is interesting if it contains an even number of palindromes. The range [L, R], with L ≤ R, is defined as the sequence of integers from L to R (inclusive): (L, L+1, L+2, ..., R-1, R). L and R are the range's first and last numbers. The range [L₁,R₁] is a subrange of [L,R] if L ≤ L₁ ≤ R₁ ≤ R. Your job is to determine how many interesting subranges of [L,R] there are.

Input

The first line of input gives the number of test cases, T. T test cases follow. Each test case is a single line containing two positive integers, L and R (in that order), separated by a space.

Output

For each test case, output one line. That line should contain "Case #x: y", where x is the case number starting with 1, and y is the number of interesting subranges of [L,R], modulo 1000000007.

Limits

Time limit: 45 6 seconds per test set.

Memory limit: 1 GB.

1 ≤ T ≤ 120

Small dataset (9 Points)

1 ≤ L ≤ R ≤ 10¹³

Large dataset (23 Points)

1 ≤ L ≤ R ≤ 10¹⁰⁰

Sample

3
1 2
1 7
12 110

Case #1: 1
Case #2: 12
Case #3: 2466