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)

/*********************************************************************************************/
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//                      \ .-\__ `-` ___/-. /                                                 //
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//                ."" '< `.___\_<|>_/___.' >'"".                                             //
//               | | : `- \`.;`\ _ /`;.`/ - ` : | |                                          //
//                 \ \ `-. \_ __\ /__ _/ .-` / /                                             //
//         ======`-.____`-.___\_____/___.-`____.-'======                                     //
//                            `=---='                                                        //
//                                                       //                                  //
//         .............................................                                     //
//                  ·ð×æ±£ÓÓ             ÓÀÎÞBUG                                            //
********************************************************************************************/
#include<iostream>
#include<cstdlib>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
using namespace std;
const long long MOD=1000000009;
const long long mod = 1e5+50;
typedef long long ll;
long long a[mod],b[mod];
int main()
{
    long long t;
    cin>>t;
    while(t--)
    {
        long long a,b;
        cin>>a>>b;
        if(a*b==3)
        {
            cout<<'1'<<endl;
            continue;
        }
        long long l=sqrt(a*b),cnt=0;
        cnt=(l-1)*2;
        if(l!=min(a,b)&&l*l<a*b)
        {
            cnt+=1;
            if((a*b-1)/l!=(a*b-1)/(l-1)&&(a*b-1)/l>l)
                cnt+=1;
        }
        if(l>min(a,b))
            cnt=cnt-1;
        cout<<cnt<<endl;
    }
    return 0;
}