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: Accepted)

#pragma comment(linker, "/STACK:102400000,102400000")
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <map>
#include <set>
#include <queue>
 
#define LL long long
 
using namespace std;
 
int a, b;
 
int main()
{
	//freopen("test_in.txt", "r", stdin);
	//freopen("test_out.txt", "w", stdout);
	int t;
	cin>>t;
	while(t--)
	{
		cin>>a>>b;
		LL p = 1ll*a*b-1, x;
		for(x = sqrt(p)-2; x <= sqrt(p)+2; x++)
			if(x*x<=p && (x+1)*(x+1) > p)	break;
		LL ans = x*2-(a<=x)-(b<=x)-(1ll*x*x<=p && 1ll*x*(x+1)>p);
		cout<<ans<<endl;
	}
}