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 = 'import math\ndef check(n):\n\tif n<9:\n\t\treturn n\n\telse:\n\t\tans = n%9\n\t\tif ans==0:\n\t\t\treturn 9\n\t\treturn ans\t\t\n\nt = int(input())\nwhile t>0:\n\tt -= 1\n\tsum = 0\n\ta,d,l,r = input().split()\n\ta,d,l,r = int(a),int(d),int(l),int(r)\n\tdig = r-l+1\n\tmod = dig%9\n\tdiv = int(dig/9)\n\tnth = a+(l-1)*d                                          \n\tnth = check(nth)\n\ttemp = 0\n\tfor i in range(l,min(l+8,r)+1):\n\t\ttemp += 1\n\t\tmul = 0 if temp>mod else 1\n\t\tsum += nth*(div+mul)\n\t\tnth = check(nth+d)\n\tprint(int(sum))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13421