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 = 'def dsum(n):\r\n    ddsum=0\r\n    while(n!=0):\r\n        a=int(n%10)\r\n        ddsum=ddsum+a\r\n        n=int(n/10)\r\n    return ddsum   \r\n\r\nfor _ in range(0,int(input())):\r\n    l=[]\r\n    a,b=map(int,input().split())\r\n    minval=1000000000\r\n    val=a\r\n    cnt=0\r\n    inv=0\r\n    l.append([])\r\n    l[inv].append(val)\r\n    l[inv].append(cnt)\r\n    if(minval>val):\r\n        minval=val\r\n        fcnf=cnt\r\n    for j in range(0,50000):\r\n        q=l.pop(0)\r\n        inv-=1\r\n        l.append([])\r\n        cnt=q[1]+1\r\n        inv+=1\r\n        l[inv].append(q[0]+b)\r\n        l[inv].append(cnt)\r\n        if(minval>(q[0]+b)):\r\n            minval=(q[0]+b)\r\n            fcnf=cnt\r\n        #print(l)    \r\n        if(q[0]>9):\r\n            p=dsum(q[0])\r\n            l.append([])\r\n            inv+=1\r\n            l[inv].append(p)\r\n            l[inv].append(cnt)\r\n            if(minval>p):\r\n                minval=p\r\n                fcnf=cnt\r\n    print(minval,fcnf)            \r\n\r\n\r\n                 \r\n                    \r\n\r\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 3377204