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: Runtime Error)

#include <iostream>
using namespace std;
int main() {
  int Q;
  cin >> Q;
  int a, b;
  for(int i = 0; i < Q; ++i) {
    cin >> a >> b;
    int M = a*b;
    int max = a > b? a : b;
    if(a > b) {
      swap(a,b);
    }
    int counter = 0;
    bool lst[M];
    for(int j = 0; j < a; ++j) {
      lst[j] = false;
    }
    for(int B = M; B != 0; --B) {
      for(int A = 1; A*B < M; ++A) {
        if(!lst[A] && A != a && B != b) {
          lst[A] = true;
          ++counter;
goto here;
        }
      }
here: ;
    }
    cout << counter << endl;
  }
  return 0;
}