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: Time Limit Exceeded)

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

namespace ConsoleApp4
{
    class Program
    {
        struct pair
        {
            public Int64 x;
            public Int64 y;
            public pair(Int64 a,Int64 b)
            {
                this.x = a;
                this.y = b;
            }
        }
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            for (int x = 0; x < N; x++)
            {
                bool same_is_included = false;
                var read = Console.ReadLine();
                int A = int.Parse(read.Split(' ')[0]);
                int B = int.Parse(read.Split(' ')[1]);
                List<pair> find = new List<pair>();
                Int64 before = 0;
                Int64 seki = A;
                seki *= B;
                Int64 output = 0;
                for (Int64 i = 1; i < seki; i++)
                {
                    Int64 sho = (seki - 1) / i;
                    if (sho != before)
                    {
                        if (i == sho) same_is_included=true;
                        if (i >sho) break;
                        pair temp = new pair(i, sho);
                        find.Add(temp);
                    }
                    before = sho;
                    
                }
                if (!same_is_included)
                {
                    for (int i = 0; i < find.Count; i++)
                    {
                        if (find[i].x != A) output++;
                        if (find[i].x != B) output++;

                    }

                }
                else
                {
                    for (int i = 0; i < find.Count-1; i++)
                    {
                        if (find[i].x != A) output++;
                        if (find[i].x != B) output++;

                    }
                    if ((find[find.Count - 1].x) != A && (find[find.Count - 1].x) != B)
                        output++;
                }

                Console.WriteLine(output);
                
            }
        }

    }
}