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: Accepted)

main()
{
  int q;scanf("%d",&q);
  for(;q--;)
  {
    long a,b;scanf("%ld%ld",&a,&b);
    if(a>b)a^=b^=a^=b;
    if(a==b||a+1==b)
    {
      printf("%ld\n",2*a-2);
    }
    else
    {
      long f=0,l=1e9;
      while(l-f>1)
      {
        long m=l+f>>1;
        if(m*m<a*b)f=m;
        else l=m;
      }
      if(f*(f+1)>=a*b)
      {
        printf("%ld\n",2*f-2);
      }
      else
      {
        printf("%ld\n",2*f-1);
      }
    }
  }
}