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.Text;

public class Program
{
    private int Q;

    public void Solve()
    {
        var sc = new Scanner();
        Q = sc.NextInt();
        var sb = new StringBuilder();
        for (int i = 0; i < Q; i++)
        {
            sb.AppendLine(Query(sc.NextLong(), sc.NextLong()).ToString());
        }

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

    private long Query(long a, long b)
    {
        if (a == b)
        {
            return (a + b) - 2;
        }

        if (a > b)
        {
            return Query(b, a);
        }
        // a <= b

        // ab両方大きいのは有り得ない cdとする
        // どっちかは小さい

        long ans = 0;

        // (c-1)(d+1) <= cd (c <= d+1)
        // 1回目が小さかった人
        ans += a - 1;

        // 2回目が小さかった人 
        // (c+1)(d-1) = cd + d - c - 1

        // t^2 < ab
        long t = (long) Math.Floor(Math.Sqrt(a * b));

        // t(t+1) < abなら cdの和は1増やせる
        long sum;
        if (t * t == a * b)
        {
            sum = t + t - 1;
        }
        else if (t * (t + 1) < a * b)
        {
            sum = t + t + 1;
        }
        else
        {
            sum = t + t;
        }

        //合計がsum cがa強 dがb未満

        // dがsum-(a+1
        ans += Math.Max(0, Math.Min(b - 1, sum - (a + 1)));
        return ans;
    }

    public static void Main(string[] args)
    {
        new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _pos = 0;
        _line = new string[0];
    }

    const char Separator = ' ';
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = Console.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = Console.ReadLine().Split(Separator);

        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}