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.Linq;
using static System.Math;

class D
{
	static void Main() => Console.WriteLine(string.Join("\n", new int[int.Parse(Console.ReadLine())].Select(_ => Console.ReadLine().Split().Select(int.Parse).ToArray()).Select(x => Find(x[0], x[1]))));

	static double Find(long a, long b)
	{
		for (long r = 0, t, c = 2 * (long)Floor(Sqrt(a * b)); ; r = t, c++)
			if ((t = Try(a, b, c)) < r) return r;
	}

	// l: x + y = c
	static long Try(long a, long b, long c) => c % 2 == 0 ?
		c * c / 4 <= a * b ? c - 2 - (a != b && c * c / 4 == a * b ? 1 : 0) : 0 :
		c / 2 * (c / 2 + 1) < a * b ? c - 2 : 0;
}