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.

Example

Input

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

Output

1
12
4
11
14
57
31
671644785

见题面

见题面