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: Wrong Answer)

using System;

namespace abc093d
{
    class Program
    {
        static void Main(string[] args)
        {
            int q = int.Parse(Console.ReadLine());
            for (int i = 0; i < q; i++)
            {
                string[] query = Console.ReadLine().Split(' ');
                long a = long.Parse(query[0]);
                long b = long.Parse(query[1]);
                double root = Math.Sqrt(a * b);
                double round = Math.Ceiling(root) - 1;
                long ans = Convert.ToInt64(round) * 2 - 1;

                long big = Math.Max(a, b);
                long small = Math.Min(a, b);

                if (round * (round + 1) > a * b)
                {
                    ans -= 1;
                }

                if (big == small)
                {
                    ans += 1;
                }
                else if (big == small + 1)
                {
                    ans -= 1;
                }

                Console.WriteLine(root);
                Console.WriteLine(ans);
            }
        }
    }
}