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<bits/stdc++.h>
#define mp make_pair
#define rep(i,n) for(int i=0;i<n;i++)
#define BINF 0x7fffffff
#define INF 0x3f3f3f3f
#define LINF 9223372036854775807
#define END(s) {cout<<s;return 0;}
#define CON(s) {cout<<s;continue;}
#define BRE(s) {cout<<s;break;}
#define pb push_back
#define all(a) a.begin(),a.end()
#define sz(a) (int)a.size()
#define F first
#define S second
#define LOCAL_JUDGE 1 //remember to change
using namespace std;
int main(){
	int t;
	cin>>t;
	rep(HateAtcoder,t){
		long long x,y;
		cin>>x>>y;
		long long pro=x*y;
		long long sq=floor(sqrt(pro));
		long long cnt=sq*2-1;
		if(sq*sq==pro) cnt--;
		if(sq>=x) cnt--;
		if(sq>=y) cnt--;
		if(sq*(sq+1)<pro) cnt++;
		cout<<cnt<<endl;
	}
	return 0;
}