Note : This question carries $150$ $points$
There is an outcry in Middle Earth, as the greatest war between Orgs of Dark Lord Sauron and Frodo Baggins is about to begin. To end the war, Frodo decides to destroy the ring in the volcano of Mordor. There are many ships that lead Frodo to Mordor, and he is confused about which one he should board.  Given two-ship numbers $M$ and $N$, Frodo has to solve a problem to find the ship which he should board.
Find the number of pairs (x, y), such that $1<=x<=M$ and $1<=y<=N$, for which $x*y + x+ y = string(x)+string(y)$ is true. 
Also, calculate the number of distinct x satisfying the given condition.  The number of pairs and the number of distinct x will help select Frodo the boat he should board. Help Frodo defeat Sauron. 

-----Input :-----
- First line contains $T$ as number of test cases 
- Each test case contains two integers $M$ and $N$ 

-----Output :-----
- For each test case, print two integers - the number of such pairs (x,y) and the number of distinct x

-----Constraints :-----
- 1 ≤ T ≤ 5000
- 1 ≤  M, N ≤ 10^9

-----Sample Input :-----
1
1 9

-----Sample Output :-----
1 1

-----Explanation :-----
For test case two M=1 and N=9  Pair (1,9) satisfies the above condition 1*9+1+9= “19” and only x=1 satisfies the equation.

```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 = 'for i in range(int(input())):\r\n    m,n = list(map(int,input().split()))\r\n    if n<9:\r\n        print(0,0)\r\n        continue\r\n    k = len(str(n))\r\n    if n==int(str(9)*k):\r\n        ans = k\r\n    else:\r\n        ans = k-1\r\n    print(m*ans,m)\r\n    #     res = min(m,n)\r\n    #     res1 = res\r\n    #     k+=1\r\n    # else:\r\n    #     res1 = \r\n\r\n    # n = n//10\r\n    # j = 1\r\n    # while n>0:\r\n    #     if ans==0:\r\n    #         ans = 9*(k-j)\r\n    #     else:\r\n    #         temp = (ans*10+9)*(k-j)\r\n    #         ans = ans+ min(temp,m)\r\n    #     j+=1\r\n    #     n = n//10\r\n    # ans = ans+res\r\n    # print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13079