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)

#include<iostream>
using namespace std;

int T;

int main()
{
	scanf("%d",&T);
	while(T--)
	{
		int a,b;
		scanf("%d%d",&a,&b);
		if(a==b)
		{
			printf("%d\n",a*2-2);
			continue;
		}
		if(a>b)
			swap(a,b);
		long long x=1LL*a*b;
		int l=0,r=b;
		while(r-l>1)
		{
			int m=(l+r)>>1;
			int A=a+1,B=m;
			int C=A+(B-A)/2;
			if(1LL*C*(A+B-C)<x)
				l=m;
			else
				r=m;
		}
		printf("%d\n",a-1+l);
	}
	return 0;
}