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 ≤ 105
- 1 ≤ A1 ≤ 109
- 0 ≤ D ≤ 109
- 1 ≤ R ≤ 1018
- 1 ≤ L ≤ R

-----Subtasks-----
- Subtask 1:  0 ≤ D ≤ 100, 1 ≤ A1 ≤ 109, 1 ≤ R ≤ 100  - 15 points
- Subtask 2:  0 ≤ D ≤ 109, 1 ≤ A1 ≤ 109, 1 ≤ R ≤ 106  - 25 points
- Subtask 3: Original constraints - 60 points

-----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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '\ncases = int(input())\n\nfor i in range(cases):\n    a1, d, uG, oG = list(map(int, input().split()))\n    a1 = a1 %9 if a1 %9 != 0 else 9\n    d = d %9 if d %9 != 0 else 9\n    sum_of = 0\n    rest_of = 0\n    q = (a1 +d *(uG -1)) %9 if (a1 +d *(uG -1)) %9 !=0 else 9\n    q1 = q\n    k = (oG - uG) %9\n    f = int((oG - uG) /9)\n    \n    for j in range(uG, uG +9):\n        sum_of += q\n        q += d\n        q = q %9 if q %9 != 0 else 9\n    \n    for k in range(uG, uG +k +1):\n        rest_of += q1\n        q1 += d\n        q1 = q1 %9 if q1 %9 != 0 else 9\n\n    print(sum_of *f +rest_of)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13323