Problem:
Score : 700 points

Problem Statement

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 1

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

Sample Output 1

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.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns #-}
import Data.Bits ((.&.),unsafeShiftL, unsafeShiftR)

import Control.Monad
import Control.Monad.ST
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as MV

main=do
  n<-readLn::IO Int
  as<-unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine::IO[Int]
  bs<-unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine::IO[Int]
  --
  print.sum.map (st n as bs) $ [0..28]
--

st::Int->[Int]->[Int]->Int->Int
st n as bs' k = if even$ sum $ map (\a->f n v k2 (a .&. km)) as then 0 else k2
  where
    k2 = unsafeShiftL 1 k
    km = (unsafeShiftL 1 (k+1)) - 1
    !v = bmod $ map (\b->b .&. km) bs'

bmod:: [Int]->V.Vector Int
bmod bs = runST $ do
  v <- V.thaw $ V.fromList bs
  sortv v 0 (MV.length v - 1)
  V.unsafeFreeze v
--
f::Int->V.Vector Int->Int->Int->Int
f n bs t a = b2 - b1 + n - b3
  where
    b1 = ubound bs (t-1-a) (-1,n)
    b2 = ubound bs ((unsafeShiftL t 1)-1-a) (-1,n)
    b3 = ubound bs ((unsafeShiftL t 2)-1-a) (-1,n)
--    b4 = ubound bs (4*t-1-a) (-1,n)

ubound v k (a,b)
    | a+1 == b = b
    | V.unsafeIndex v m <= k = ubound v k (m,b)
    | True = ubound v k (a,m)
    where m = unsafeShiftR (a+b) 1
--
{-# INLINE sortv #-}
sortv :: MV.STVector s Int -> Int -> Int -> ST s ()
sortv as b e = do
        l <- MV.unsafeRead as b
        r <- MV.unsafeRead as e
        p <- findP l (b+1) e
        case p of
            Nothing -> return ()
            Just piv -> do
                k <- partv as piv b e
                sortv as b (k-1)
                sortv as k e
    where
        findP a i e
            | i > e = return Nothing
            | True = do
                k <- MV.unsafeRead as i
                case (a < k, k < a) of
                    (True, _) -> return $ Just k
                    (_, True) -> return $ Just a
                    _ -> findP a (i+1) e

partv :: MV.STVector s Int -> Int -> Int -> Int -> ST s Int
partv as piv b e = do
    MV.unsafeSwap as b e
    l <- findF b
    r <- findT e
    if l <= r then partv as piv l r
              else return l
    where
        findF i = do
            k <- MV.unsafeRead as i
            if k < piv then findF (i+1) else return i
        findT j = do
            k <- MV.unsafeRead as j
            if k < piv then return j else findT (j-1)