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())\nfor it in range(q):\n    a, b = list(map(int, input().split()))\n    if a * b <= 2:\n        print((0))\n        continue\n    lo, hi = 1, a*b - 1\n    while lo < hi:\n        x = (lo + hi + 1) // 2\n        #l = list(range(max(1, x // 2 - 2), x // 2 + 3))\n        #r = list(range(max(1, x // 2 - 2), x // 2 + 3))\n        if x % 2 == 0:\n            r1, r2 = x // 2, x // 2 + 1\n            l1, l2 = x // 2, x // 2 + 1\n        else:\n            l, r = (x + 1) // 2, (x + 1) // 2 \n            if a <= l:\n                l += 1\n            if b <= r:\n                r += 1\n            if l * r < a * b:\n                lo = x\n            else:\n                hi = x - 1\n            continue\n        if b <= r1:\n            r1 += 1\n            r2 += 1\n        #elif b >= r2 and b <= x:\n        #    r1 -= 1\n        #    r2 -= 1\n        if a <= l1:\n            l1 += 1\n            l2 += 1\n        #elif a >= l2 and a <= x:\n        #    l1 -= 1\n        #    l2 -= 1\n        if l1 * r2 < a*b and l2 * r1 < a*b:\n            lo = x\n        else:\n            hi = x - 1\n    print(lo)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13365