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)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int main(void){
  unsigned long long int score, pre, ans, r, j;
  int q, a, b, i, dis, t;
  scanf("%d",&q);
  for(i=0;i<q;i++){
    scanf("%d %d",&a, &b);
    if(a<b){t=a; a=b; b=t;}
    score = (unsigned long long int) a*b;
    pre = -1;  dis=0;
    //printf("%d: s=%llu\n",i,score);
    for(j=sqrt(score); ;j++){
      r=score/j;
      if(score%j==0) r--;
      if(r==pre) break;
      if(j==a || r==b) dis++;
      else pre=r;
      //printf("%llu->",r);
    }
    //printf(".\n");
    if(r>b) dis++;
    ans = r+j-2-dis;
    printf("%llu\n",ans);
  }

  return 0;
}