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;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static IEnumerable<long> Solve(int Q, int[][] V)
        {
            var list = new List<long>();
            for (int i = 0; i < Q; ++i)
            {
                int A = Math.Min(V[i][0], V[i][1]);
                int B = Math.Max(V[i][0], V[i][1]); ;
                if (B - A <= 1)
                {
                    list.Add((A - 1) * 2);
                }
                else
                {
                    long N = Math.BigMul(A, B);
                    long n = (long)Math.Ceiling(Math.Sqrt(N) - 1.0);
                    list.Add((n * (n + 1) < N) ? n * 2 - 1 : n * 2 - 2);
                }
            }
            return list;
        }
        static void Main(string[] args)
        {
            int Q = ReadInt();
            var V = new int[Q][];
            for (int i = 0; i < Q; ++i) { V[i] = ReadInts(); }
            foreach (long ans in Solve(Q, V))
            {
                Console.WriteLine(ans);
            }
        }
    }
}