Solve the programming task below in a Python markdown code block.
Read problems statements in Mandarin Chinese, Russian and Vietnamese as well. 

Eugene loves sequences, especially arithmetic progressions. One day he was asked to solve a difficult problem.

If a sequence of numbers A_{1}, A_{2}, ... , A_{N} form an arithmetic progression A, he was asked to calculate sum of F(A_{i}), for L ≤ i ≤ R.
F(X) is defined as:

If X < 10 then F(X) = X.

Else F(X) = F(sum_{of}_digits(X)).

Example:

F(1378) = 
F(1+3+7+8) = 
F(19) = 
F(1 + 9) = 
F(10) = 
F(1+0) = 
F(1) = 1

------ Input ------ 

The first line of the input contains an integer T denoting the number of test cases.
Each test case is described in one line containing four integers: A_{1} denoting the first element of the arithmetic progression A, D denoting the common difference between successive members of A, and L and R as described in the problem statement.

------ Output ------ 

For each test case, output a single line containing one integer denoting sum of F(A_{i}).

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$1 ≤ A_{1} ≤ 10^{9}$
$0 ≤ D ≤ 10^{9}$
$1 ≤ R ≤ 10^{18}$
$1 ≤ L ≤ R$

------ Subtasks ------ 

$Subtask 1:  0 ≤ D ≤ 100, 1 ≤ A_{1} ≤ 10^{9}, 1 ≤ R ≤ 100  - 15 points$

$Subtask 2:  0 ≤ D ≤ 10^{9}, 1 ≤ A_{1} ≤ 10^{9}, 1 ≤ R ≤ 10^{6}  - 25 points$

$Subtask 3: Original constraints - 60 points$

----- Sample Input 1 ------ 
2

1 1 1 3

14 7 2 4
----- Sample Output 1 ------ 
6

12
----- explanation 1 ------ 
Example case 1.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}
A1 = 1
A2 = 2
A3 = 3
F(A1) = 1
F(A2) = 2
F(A3) = 3
1+2+3=6

Example case 2.
A = {14, 21, 28, 35, 42, 49, 56, 63, 70, 77,  ...}
A2 = 21
A3 = 28
A4 = 35
F(A2) = 3
F(A3) = 1
F(A4) = 8
3+1+8=12