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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Convert;
using static System.Math;
using static Constants;
using static Extensions;
using static MathExtensions;

public class Program
{
    public static void Solve()
    {
        var q = I;

        foreach (var _ in Range(q))
        {
            var a = L;
            var b = L;
            var ans = BinarySearch.Search(x =>
            {
                if (x % 2 == 0)
                {
                    var amid0 = x / 2;
                    var amid1 = x / 2 + 1;
                    if (amid0 >= a) amid0++;
                    if (amid1 >= a) amid1++;
                    var bmid1 = x / 2 + 1;
                    var bmid0 = x / 2;
                    if (bmid1 >= b) bmid1++;
                    if (bmid0 >= b) bmid0++;
                    return amid0 * bmid1 < a * b && amid1 * bmid0 < a * b;
                }
                else
                {
                    var amid = x / 2 + 1;
                    if (amid >= a) amid++;
                    var bmid = x / 2 + 1;
                    if (bmid >= b) bmid++;
                    return amid * bmid < a * b;
                }
            },
            (long)int.MaxValue, 0);

            Console.WriteLine(ans);
        }
    }

    #region Scanners
    static TextScanner _ts;

    static char C => char.Parse(_ts.Next());
    static string S => _ts.Next();
    static int I => int.Parse(_ts.Next());
    static long L => long.Parse(_ts.Next());
    static BigInteger B => BigInteger.Parse(_ts.Next());
    static double D => double.Parse(_ts.Next());

    static char[] Cs(int count) => Repeat(count, () => C).ToArray();
    static string[] Ss(int count) => Repeat(count, () => S).ToArray();
    static int[] Is(int count) => Repeat(count, () => I).ToArray();
    static long[] Ls(int count) => Repeat(count, () => L).ToArray();
    static BigInteger[] Bs(int count) => Repeat(count, () => B).ToArray();
    static double[] Ds(int count) => Repeat(count, () => D).ToArray();
    #endregion

    [DebuggerStepThrough]
    public static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput());
        sw.NewLine = "\n";
#if DEBUG
        sw.AutoFlush = true;
#else
        sw.AutoFlush = false;
#endif
        Console.SetOut(sw);
        _ts = new TextScanner(Console.In);
        Solve();
        Console.Out.Flush();
    }
}

public static class BinarySearch
{
    public static int LowerBound<T>(this IReadOnlyList<T> source, T value)
        where T : IComparable<T>
        => source.LowerBound(value, Comparer<T>.Default);

    public static int LowerBound<T>(this IReadOnlyList<T> source, T value, IComparer<T> comparer)
        => LowerBound(i => source[i], 0, source.Count - 1, value, comparer);

    public static int LowerBound<T>(Func<int, T> func, int minValue, int maxValue, T value)
        where T : IComparable<T>
        => LowerBound(func, minValue, maxValue, value, Comparer<T>.Default);

    public static long LowerBound<T>(Func<long, T> func, long minValue, long maxValue, T value)
        where T : IComparable<T>
        => LowerBound(func, minValue, maxValue, value, Comparer<T>.Default);

    public static BigInteger LowerBound<T>(Func<BigInteger, T> func, BigInteger minValue, BigInteger maxValue, T value)
        where T : IComparable<T>
        => LowerBound(func, minValue, maxValue, value, Comparer<T>.Default);

    public static int LowerBound<T>(Func<int, T> func, int minValue, int maxValue, T value, IComparer<T> comparer)
    {
        var i = Search(x => comparer.Compare(func(x), value) >= 0, minValue, maxValue);
        return comparer.Compare(func(i), value) < 0 ? i + 1 : i;
    }

    public static long LowerBound<T>(Func<long, T> func, long minValue, long maxValue, T value, IComparer<T> comparer)
    {
        var i = Search(x => comparer.Compare(func(x), value) >= 0, minValue, maxValue);
        return comparer.Compare(func(i), value) < 0 ? i + 1 : i;
    }

    public static BigInteger LowerBound<T>(Func<BigInteger, T> func, BigInteger minValue, BigInteger maxValue, T value, IComparer<T> comparer)
    {
        var i = Search(x => comparer.Compare(func(x), value) >= 0, minValue, maxValue);
        return comparer.Compare(func(i), value) < 0 ? i + 1 : i;
    }

    public static int UpperBound<T>(this IReadOnlyList<T> source, T value)
        where T : IComparable<T>
        => source.UpperBound(value, Comparer<T>.Default);

    public static int UpperBound<T>(this IReadOnlyList<T> source, T value, IComparer<T> comparer)
        => UpperBound(i => source[i], 0, source.Count - 1, value, comparer);

    public static int UpperBound<T>(Func<int, T> func, int minValue, int maxValue, T value)
        where T : IComparable<T>
        => UpperBound(func, minValue, maxValue, value, Comparer<T>.Default);

    public static long UpperBound<T>(Func<long, T> func, long minValue, long maxValue, T value)
        where T : IComparable<T>
        => UpperBound(func, minValue, maxValue, value, Comparer<T>.Default);

    public static BigInteger UpperBound<T>(Func<BigInteger, T> func, BigInteger minValue, BigInteger maxValue, T value)
        where T : IComparable<T>
        => UpperBound(func, minValue, maxValue, value, Comparer<T>.Default);

    public static int UpperBound<T>(Func<int, T> func, int minValue, int maxValue, T value, IComparer<T> comparer)
    {
        var i = Search(x => comparer.Compare(func(x), value) > 0, minValue, maxValue);
        return comparer.Compare(func(i), value) <= 0 ? i + 1 : i;
    }

    public static long UpperBound<T>(Func<long, T> func, long minValue, long maxValue, T value, IComparer<T> comparer)
    {
        var i = Search(x => comparer.Compare(func(x), value) > 0, minValue, maxValue);
        return comparer.Compare(func(i), value) <= 0 ? i + 1 : i;
    }

    public static BigInteger UpperBound<T>(Func<BigInteger, T> func, BigInteger minValue, BigInteger maxValue, T value, IComparer<T> comparer)
    {
        var i = Search(x => comparer.Compare(func(x), value) > 0, minValue, maxValue);
        return comparer.Compare(func(i), value) <= 0 ? i + 1 : i;
    }

    public static int Search(Func<int, bool> predicate, int minValue, int maxValue)
    {
        var ok = maxValue;
        var ng = minValue - 1;

        while (System.Math.Abs(ok - ng) > 1)
        {
            var mid = (ok + ng) / 2;
            if (predicate(mid)) ok = mid;
            else ng = mid;
        }

        return ok;
    }

    public static long Search(Func<long, bool> predicate, long minValue, long maxValue)
    {
        var ok = maxValue;
        var ng = minValue - 1;

        while (System.Math.Abs(ok - ng) > 1)
        {
            var mid = (ok + ng) / 2;
            if (predicate(mid)) ok = mid;
            else ng = mid;
        }

        return ok;
    }

    public static BigInteger Search(Func<BigInteger, bool> predicate, BigInteger minValue, BigInteger maxValue)
    {
        var ok = maxValue;
        var ng = minValue - 1;

        while (BigInteger.Abs(ok - ng) > 1)
        {
            var mid = (ok + ng) / 2;
            if (predicate(mid)) ok = mid;
            else ng = mid;
        }

        return ok;
    }
}

[DebuggerStepThrough]
public class TextScanner
{
    private readonly TextReader _tr;

    public TextScanner(TextReader tr)
    {
        _tr = tr;
    }

    public string Next()
    {
        var sb = new StringBuilder();
        int i;
        do
        {
            i = _tr.Read();
            if (i == -1) throw new EndOfStreamException();
        }
        while (char.IsWhiteSpace((char)i));
        while (i != -1 && !char.IsWhiteSpace((char)i))
        {
            sb.Append((char)i);
            i = _tr.Read();
        }
        return sb.ToString();
    }
}

public static class Constants
{
    public const int AnswerToLifeTheUniverseAndEverything = 42;
    public const string Yes = "Yes";
    public const string No = "No";
    public const string YES = "YES";
    public const string NO = "NO";
    public const string Possible = "Possible";
    public const string Impossible = "Impossible";
    public const string POSSIBLE = "POSSIBLE";
    public const string IMPOSSIBLE = "IMPOSSIBLE";
}

[DebuggerStepThrough]
public static class Extensions
{
    public static void Answer(object value)
    {
        Console.WriteLine(value);
        Exit(0);
    }

    public static void Assert(bool condition)
    {
        if (!condition) throw new Exception("Assertion failed");
    }

    public static string AsString(this IEnumerable<char> source) => new string(source.ToArray());

    public static Dictionary<T, int> Bucket<T>(this IEnumerable<T> source) where T : IEquatable<T>
    {
        var dict = new Dictionary<T, int>();
        foreach (var item in source) if (dict.ContainsKey(item)) dict[item]++; else dict[item] = 1;
        return dict;
    }

    public static int[] Bucket<T>(this IEnumerable<T> source, int maxValue, Func<T, int> selector)
    {
        var arr = new int[maxValue + 1];
        foreach (var item in source) arr[selector(item)]++;
        return arr;
    }

    public static IComparer<T> CreateDescendingComparer<T>()
        where T : IComparable<T>
        => Comparer<T>.Create((x, y) => y.CompareTo(x));

    public static IEnumerable<int> CumSum(this IEnumerable<int> source)
    {
        var sum = 0;
        foreach (var item in source) yield return sum += item;
    }

    public static IEnumerable<long> CumSum(this IEnumerable<long> source)
    {
        var sum = 0L;
        foreach (var item in source) yield return sum += item;
    }

    public static void Exit(int exitCode)
    {
        Console.Out.Flush();
        Environment.Exit(exitCode);
    }

    public static void ForEach<T>(this IEnumerable<T> source, Action<T> action)
    {
        foreach (var item in source) action(item);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, _> func)
    {
        foreach (var item in source) func(item);
    }

    public static void ForEach<T>(this IEnumerable<T> source, Action<T, int> action)
    {
        var i = 0;
        foreach (var item in source) action(item, i++);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, int, _> func)
    {
        var i = 0;
        foreach (var item in source) func(item, i++);
    }

    // [l, r)
    public static bool IsIn<T>(this T value, T l, T r)
        where T : IComparable<T>
    {
        if (l.CompareTo(r) > 0) throw new ArgumentException();
        return l.CompareTo(value) <= 0 && value.CompareTo(r) < 0;
    }

    public static IEnumerable<int> Range(int start, int end, int step = 1)
    {
        for (var i = start; i < end; i += step) yield return i;
    }

    public static IEnumerable<int> Range(int end) => Range(0, end);

    public static void Repeat(int count, Action action)
    {
        for (var i = 0; i < count; i++) action();
    }

    public static void Repeat(int count, Action<int> action)
    {
        for (var i = 0; i < count; i++) action(i);
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<T> func)
    {
        for (var i = 0; i < count; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<int, T> func)
    {
        for (var i = 0; i < count; i++) yield return func(i);
    }

    public static IEnumerable<int> RangeReverse(int start, int end, int step = 1)
    {
        for (var i = end - 1; i >= start; i -= step) yield return i;
    }

    public static IEnumerable<int> RangeReverse(int end) => RangeReverse(0, end);

    public static void Swap<T>(ref T x, ref T y)
    {
        var tmp = x; x = y; y = tmp;
    }
}

[DebuggerStepThrough]
public static class MathExtensions
{
    public static int DivCeil(int left, int right)
        => left / right + (left % right == 0 ? 0 : 1);

    public static long DivCeil(long left, long right)
        => left / right + (left % right == 0L ? 0L : 1L);

    public static int Gcd(int left, int right)
    {
        int r;
        while ((r = left % right) != 0) { left = right; right = r; }
        return right;
    }

    public static long Gcd(long left, long right)
    {
        long r;
        while ((r = left % right) != 0L) { left = right; right = r; }
        return right;
    }

    public static BigInteger Gcd(BigInteger left, BigInteger right)
        => BigInteger.GreatestCommonDivisor(left, right);

    public static int HighestOneBit(int x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        return x - (x >> 1);
    }

    public static long HighestOneBit(long x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        x |= x >> 32;
        return x - (x >> 1);
    }

    public static int Lcm(int left, int right) => left / Gcd(left, right) * right;

    public static long Lcm(long left, long right) => left / Gcd(left, right) * right;

    public static BigInteger Lcm(BigInteger left, BigInteger right)
        => left / Gcd(left, right) * right;

    public static int Pow(int value, int exponent)
    {
        var r = 1;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Pow(long value, int exponent)
    {
        var r = 1L;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Fact(int value)
    {
        var r = 1L;
        for (var i = 2; i <= value; i++) r *= i;
        return r;
    }
}