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 = '\ndef bsearch(target, min_i, max_i, func):\n    # func(index) <= target < func(index+1) となるindexを返す\n    if func(max_i) < target:\n        return max_i\n    if target <= func(min_i):\n        return None\n    index = (max_i + min_i)//2\n    while True:\n        if max_i - min_i <= 1:\n            return min_i\n        if func(index) < target:\n            index, min_i = (index + max_i)//2, index\n            continue\n        index, max_i = (index + min_i)//2, index\n\n\ndef f(N):\n    def g(i):\n#        print(i,I,J)\n        if i < I or J < i:\n            return i*(N-i+1)\n        elif i == I:\n            return 0\n        elif I < J:\n            return i*(N-i+2)\n        else:\n            return i*(N-i)\n    I, J = A,N-B+1\n    return max(g(N//2), g(N//2+1), g(N//2+2))\n\nQ, = list(map(int, input().split()))\nfor _ in range(Q):\n    A, B = list(map(int, input().split()))\n    r = bsearch(A*B, 1, A*B, f)\n    print((r-1))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13349