10^{10^{10}} participants, including Takahashi, competed in two programming contests.
In each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.
The score of a participant is the product of his/her ranks in the two contests.
Process the following Q queries:
 - In the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.

-----Constraints-----
 - 1 \leq Q \leq 100
 - 1\leq A_i,B_i\leq 10^9(1\leq i\leq Q)
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
Q
A_1 B_1
:
A_Q B_Q

-----Output-----
For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.

-----Sample Input-----
8
1 4
10 5
3 3
4 11
8 9
22 40
8 36
314159265 358979323

-----Sample Output-----
1
12
4
11
14
57
31
671644785

Let us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).
In the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 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 = 'Q=int(input())\nE=10**(-10)\nfrom math import floor\ndef f(x):\n  if min(abs(int(x)-x),abs(int(x)+1-x))<E:\n    return int(x-1)\n  else:\n    return int(x)\n  \nfor i in range(Q):\n  a,b=list(map(int,input().split()))\n  n=a*b\n  if f(n**(1/2))<a and f(n**(1/2))<b:\n    if f(n**(1/2))*(f(n**(1/2))+1)<n:\n      print((2*f(n**(1/2))))\n    else:\n      print((2*f(n**(1/2))-1))\n  else:\n    if f(n**(1/2))*(f(n**(1/2))+1)<n:\n      print((2*f(n**(1/2))-1))\n    else:\n      print((2*f(n**(1/2))-2))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13389