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;

class Solution
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var anwer = new StringBuilder();
        for (int i = 0; i < n; i++)
        {
            var q = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            var score = q[0] * q[1] - 1;
            var r = (long)(Math.Sqrt(score)) + 1;
            while (r > 0 && r * r > score)
            {
                r--;
            }

            long count = r * 2 - q.Distinct().Count(qq => qq <= r);
            if (r != 0 && score / r == r)
            {
                count--;
            }
            anwer.AppendLine(count.ToString());
        }

        Console.Write(anwer.ToString());
    }
}