Given two side lengths, determine whether they can form a triangle with some positive third side, and if so provide a valid choice.
Problem
You are given two positive integers representing two side lengths of a triangle. Your task is to determine whether there exists a positive integer value for the third side so that the three sides can form a non-degenerate triangle.
A triangle is valid only if the sum of every pair of sides is strictly greater than the remaining side.
If such a third side exists, output any valid positive integer value for it. If no such value exists, output -1.
Notes
- A non-degenerate triangle must satisfy all three strict triangle inequalities.
- You do not need to maximize or minimize the third side unless needed to produce a valid answer.
- Any valid integer third side is acceptable.
Input Format
- The first line contains an integer
t, the number of test cases. - Each of the next
tlines contains two integersaandb.
Output Format
For each test case, print one integer:
- a valid third side length, or
-1if no valid triangle can be formed.
Constraints
1 <= t <= $10^{4}$1 <= a, b <= $10^{9}$- The third side, if it exists, should be a positive integer.
Hints
- A triangle needs the third side to be less than
a + band greater than|a-b|. - Since you only need any valid integer, look for a simple value that always works when possible.
Input Format
- The first line contains
t. - Each of the next
tlines contains two integersaandb.
Output Format
For each test case, print one integer on a separate line: a valid third side or -1.
Constraints
1 <= t <= $10^{4}$1 <= a, b <= $10^{9}$- Output must be a positive integer when a triangle is possible.
Example 1
Input
3 3 4 1 1 2 10
Output
2 1 -1
Explanation
For (3, 4), 2 works because 3 + 2 > 4, 4 + 2 > 3, and 3 + 4 > 2.
For (1, 1), 1 forms an equilateral triangle.
For (2, 10), no positive integer third side can satisfy 2 + x > 10 and 2 + 10 > x simultaneously with the remaining inequality.
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