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

If a sequence of numbers A1, A2, ... , AN form an arithmetic progression A, he was asked to calculate sum of F(Ai), 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: A1 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(Ai).

Constraints

1 ≤ T ≤ 10^5
1 ≤ A1 ≤ 10^9
0 ≤ D ≤ 10^9
1 ≤ R ≤ 10^18
1 ≤ L ≤ R

Example
Input:
2
1 1 1 3
14 7 2 4

Output:
6
12

Explanation
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

见题面

见题面