You are given positive integers $N$ and $D$. You may perform operations of the following two types:
- add $D$ to $N$, i.e. change $N$ to $N+D$
- change $N$ to $\mathop{\mathrm{digitsum}}(N)$
Here, $\mathop{\mathrm{digitsum}}(x)$ is the sum of decimal digits of $x$. For example, $\mathop{\mathrm{digitsum}}(123)=1+2+3=6$, $\mathop{\mathrm{digitsum}}(100)=1+0+0=1$, $\mathop{\mathrm{digitsum}}(365)=3+6+5=14$.
You may perform any number of operations (including zero) in any order. Please find the minimum obtainable value of $N$ and the minimum number of operations required to obtain this value.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $N$ and $D$.

-----Output-----
For each test case, print a single line containing two space-separated integers — the minimum value of $N$ and the minimum required number of operations.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N, D \le 10^{10}$

-----Subtasks-----
Subtask #1 (30 points): $1 \le N, D \le 100$
Subtask #2 (70 points): original constraints

-----Example Input-----
3
2 1
9 3
11 13

-----Example Output-----
1 9
3 2
1 4

-----Explanation-----
Example case 1: The value $N=1$ can be achieved by 8 successive "add" operations (changing $N$ to $10$) and one "digit-sum" operation.
Example case 2: You can prove that you cannot obtain $N=1$ and $N=2$, and you can obtain $N=3$.
The value $N=3$ can be achieved by one "add" and one "digitsum" operation, changing $9$ to $12$ and $12$ to $3$.  
Example case 3: $N=1$ can be achieved by operations "add", "add", "digitsum", "digitsum": $11 \rightarrow 24 \rightarrow 37 \rightarrow 10 \rightarrow 1$.

```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 = "# https://www.codechef.com/OCT18B/problems/MINDSUM\r\n'''\r\n\tAuthor - Subhajit Das\r\n\tUniversity of Engineering and Management, Kolkata\r\n\t28/1/2018\r\n'''\r\n\r\n\r\ndef sum_digits(x):\r\n    return sum(map(int, str(x)))\r\n\r\n\r\ndef main():\r\n    for _ in range(int(input())):\r\n        n, d = map(int, input().strip().split())\r\n\r\n        que = [(n, 0)]\r\n        min_track = dict()\r\n        i = 0\r\n        op_count = 0\r\n        while len(que) != 0 and i <= 1000:\r\n            i += 1\r\n            n, op_count = que.pop(0)\r\n            if n == 1:\r\n                break\r\n            if n > 1 and n <= 9:\r\n                if n not in min_track.keys():\r\n                    min_track[n] = op_count\r\n                else:\r\n                    min_track[n] = min(min_track[n], op_count)\r\n            else:\r\n                que.append((sum_digits(n), op_count+1))\r\n            que.append((n+d, op_count+1))\r\n\r\n        if n == 1:\r\n            print(n, op_count)\r\n        else:\r\n            min_key = min(min_track.keys())\r\n            print(min_key, min_track[min_key])\r\n\r\n\r\ndef __starting_point():\r\n    main()\r\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 36066