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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            //_reads = new string[] { "200000", string.Join(" ", Enumerable.Repeat("1000000000", 200000)) };
            int count = int.Parse(ReadLine());
            for (int i = 0; i < count; ++i)
            {
                Console.WriteLine(Get());
            }
        }

        static long Get()
        {
            var read = ReadLine().Split(' ').Select(long.Parse).ToArray();
            var min = Math.Min(read[0], read[1]);
            var max = Math.Max(read[0], read[1]);
            long score = read[0] * read[1];
            long sq = (long)Math.Sqrt(score);
            if (sq * sq == score) --sq;
            long result = sq - (min <= sq ? 1 : 0);
            result += sq - (max <= sq ? 1 : 0);
            if (score <= sq * (sq + 1)) --result;
            return result;
        }}}