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;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		int Q = GetInt();
		long[] A = new long[Q];
		long[] B = new long[Q];
		for(int i = 0; i < Q; i++)
		{
			A[i] = GetLong();
			B[i] = GetLong();
		}

		long[] ans = new long[Q];
		for(int i = 0; i < Q; i++)
			ans[i] = calc(A[i], B[i]);

		Console.WriteLine(string.Join("\n", ans.Select(x => x.ToString()).ToArray()));
	}

	private long calc(long A, long B)
	{
		if(A == B)
			return (2 * A - 2);

		if(A > B)
			swap(ref A, ref B);

		long T = A * B;
		long ok = 0;
		long ng = (long)1e9;
		while(Math.Abs(ng - ok) > 1)
		{
			long mid = (ng + ok) / 2;
			long max = ((mid + 1) / 2) * (mid + 1 - ((mid + 1) / 2));
			if(max < T)
				ok = mid;
			else
				ng = mid;
		}

		return ok - 1;
	}

	private void swap(ref long x, ref long y)
	{
		long tmp = x;
		x = y;
		y = tmp;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}