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;
using System.Threading.Tasks;

namespace ARC094D {
    class Program {
        static void Main(string[] args) {
            int Q = int.Parse(Console.ReadLine());
            for(int i = 0; i < Q; i++) {
                int[] input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                Array.Sort(input);
                long A = input[0];
                long B = input[1];
                long mul = A * B;
                long N = (long)Math.Floor(Math.Sqrt(mul));
                long ans = -1;
                if(N * N == mul) {
                    ans = (N - 1) * 2;
                    if(A < N) {
                        ans--;
                    }
                } else {
                    ans = N * 2 - 2;
                }
                if(N * (N + 1) < mul) {
                    ans++;
                }
                Console.WriteLine(ans);
            }
        }
    }
}