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: Runtime Error)

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <cassert>
#include <cmath>
using namespace std;
using VI = vector<long>;

int main() {
    int q;
    cin >> q;
    for (int i = 0; i < q; i++) {
        long a, b, aa, bb;
        cin >> a >> b;
        aa = min(a, b);
        bb = max(a, b);
        if (a == b) {
            cout << 2 * a - 2 << endl;
            continue;
        }
        if (aa + 1 == bb) {
            cout << 2 * aa - 2 << endl;
        } else {
            long c = sqrt(aa * bb - 1);
            assert(c * c < a * b);
            assert((c + 1) * (c + 1) >= a * b);
            if (c * (c + 1) >= aa * bb) {
                cout << 2 * c - 2 << endl;
            } else {
                cout << 2 * c - 1 << endl;
            }
        }
    }
}