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: Accepted)

#include<stdio.h>
#include<math.h>
int main() {
    double a, b,m;
    long q, i,cm,flag;
    long ans;
    scanf("%d", &q);
    for (i = 0; i < q; i++) {
        flag = 0;
        scanf("%lf%lf", &a, &b);
        if (a == b) {
            ans = (a - 1) * 2;
        }
        else {
            m = sqrt(a*b);
            cm = m;
            if (cm == m)
                cm--;
            else if (cm*(cm + 1) >= a*b)
                flag = 1;
            ans = cm * 2 - 1;
            if (flag == 1)
                ans--;
        }
        printf("%ld\n", ans);
    }
    return 0;
}