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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>
int main(){
  int q,i;
  scanf("%d",&q);
  long long a,b,c,count[q+1];
  for(i=0;i<q;i++){
    scanf("%lld%lld",&a,&b);
    c=a*b-1;
    count[i]=sqrt(c);
    if(a*b==1)
      count[i]=0;
    else if(a==1 || b==1)
      count[i]=2*count[i]-1;
    else if(a==b)
      count[i]*=2;
    else{
      if(count[i]==c/count[i])
        count[i]=2*count[i]-2;
      else
        count[i]=2*count[i]-1;
    }
  }
  for(i=0;i<q;i++)
    printf("%d\n",count[i]);
  return 0;
}