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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <cmath>
using namespace std;
typedef long long ll;
ll n, m;

int main() {
	ll q;
	cin >> q;
	for(ll i = 0; i < q; i++){
		ll a, b;
		cin >> a >> b;
		if(a > b){
			ll tmp = b;
			b = a;
			a = tmp;
		}//swap
		ll r = 2*(a-1);
		if(a < b-1){
			r++;
			ll rbuf = 0;
			ll amax = b-2;
			ll amin = a+1;
			while(amax > amin){
				if(amax*amin < a*b){
					rbuf++;
					amin++;
				}
				amax--;
			}
			r += 2*rbuf;
			if(amax == amin && amax*amin < a*b){
				r++;
			}
		}
		cout << r <<endl;
	}
	return 0;
}