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\n     \ndef f(x):\n    if x<10:\n        return x\n    n = 0\n    while x>0:\n        n+=x%10\n        x/=10\n    return f(n)\n \ndef ans(a,d,n):\n    s = 0\n    if d==0:\n        print(a*n)\n    elif d==1 or d==2 or d==4 or d==5 or d==7 or d==8:\n        if n<9:\n            while n>0:\n                s = s+a\n                a = f(a+d)\n                n = n-1\n            print(s)\n        else:\n            x = 9\n            while x>0:\n                s = s+a\n                a = f(a+d)\n                x = x-1\n            s = s*int(n/9)\n            n = n%9\n            while n>0:\n                s = s+a\n                a = f(a+d)\n                n = n-1\n            print(s)\n    elif d==3 or d==6:\n        if n<3:\n            while n>0:\n                s = s+a\n                a = f(a+d)\n                n = n-1\n            print(s)\n        else:\n            x = 3\n            while x>0:\n                s = s+a\n                a = f(a+d)\n                x = x-1\n            s = s*int(n/3)\n            n = n%3\n            while n>0:\n                s = s+a\n                a = f(a+d)\n                n = n-1\n            print(s)\n    else:\n        if a==0:\n            print(9*(n-1))\n        else:\n            print(a*n)\n\nt = int(input())\nwhile t>0:\n    a,d,l,r = list(map(int,input().split(' ')))\n    n = r-l+1\n    a = a+(l-1)*d\n    a = f(a)\n    d = f(d)\n    ans(a,d,n)\n    t-=1 "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13353