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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <unordered_set>
#include <math.h>
using namespace std;
#define inf 999999999
#define loop(i, a, b) for (int i = (a), i##len = (b); i < i##len; ++i)
#define rep(i, n) loop(i, 0, n)
#define lin long long
 
int q;
 
lin solve(lin a, lin b)
{
    if(a > b)
        swap(a,b);

    if(a == b)
        return a * 2 - 2;
    else if(a + 1 == b)
        return a * 2 - 2;

    lin ab = a * b;
    long double ldab = ab;
    long double ldc = sqrt(ldab);
    lin c = floor(ldc);

    if(c * (c + 1) >= ab)
        return c * 2 - 2;

    return c * 2 - 1;
}
 
int main(void)
{
    cin >> q;
    rep(i, q)
    {
        lin a, b;   
        cin >> a >> b;

        cout << solve(a, b) << endl;
    }
 
    return 0;
}