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.

8
1 4
10 5
3 3
4 11
8 9
22 40
8 36
314159265 358979323

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 $1$.