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 = 'def isqrt(n):\n\tL = 0\n\tR = n\n\twhile R-L > 2:\n\t\tM = (L+R)//2\n\t\tif M*M==n:\n\t\t\treturn M\n\t\telif M*M < n:\n\t\t\tL = M\n\t\telse:\n\t\t\tR = M \n\tfor ans in range(R,L-1,-1):\n\t\tif ans*ans <= n:\n\t\t\treturn ans\n\tassert(False)\n\treturn -1\ndef count(n,A,B):\n\tans = 0\n\n\tlimit = isqrt(n)\n\t# x = A + 1\n\t# while True:\n\t# \tif x*x <= n:\n\t# \t\tif n//x < B:\n\t# \t\t\tans += 1\n\t# \t\tx += 1\n\t# \telse:\n\t# \t\treturn ans + min(n//x,B-1)\n\treturn max(0,limit-A) + min(n//(limit+1),B-1)\nfor _ in range(int(input())):\n\tA, B = map(int,input().split())\n\tprint(count(A*B-1,A,B)+count(A*B-1,B,A))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13303