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)

#include <bits/stdc++.h>
using namespace std;

long long q, a, b;

long long solve();

int main() {
  cin >> q;
  for(int i = 0; i < q; ++i) {
    cin >> a >> b;
    cout << solve() << endl;
  }
  return 0;
}

long long solve() {
  if(a > b) swap(a, b);
  long long now = b - 1, cnta = 0, cntb = 0;
  cnta = a - (a + b + 1) / (b + 1);
  for(long long i = a + 1; i * i <= a * b; ++i) {
    now = a * b / i - (a * b % i == 0);
    if(now == 0) break;
    // cout << now << " " << i << " " << endl;
    ++cntb;
    --now;
  }
  cntb += now;
  return cnta + cntb + min(a - cnta - 1, b - cntb - 1);
}