# PROBLEM LINK:

Practice

Contest: Division 1

Contest: Division 2

Contest: Division 3

Contest: Division 4

* Author:* utkarsh_25dec

*IceKnight1093, tabr*

**Testers:***IceKnight1093*

**Editorialist:**# DIFFICULTY:

577

# PREREQUISITES:

None

# PROBLEM:

Given A and C, does there exist an integer B such that A, B, C are in AP?

# EXPLANATION:

For A, B, and C to be in arithmetic progression, there must exist a common difference d such that B-A = C-B = d.

This tells us that 2d = C-B + B-A = C-A, and so d = \frac{C-A}{2}.

So, the only possible value of B is A+d = A + \frac{C-A}{2} = \frac{A+C}{2}.

Under the constraints of the problem, we’d like B to be an integer. Note that \frac{A+C}{2} is an integer if and only if A+C is even. So,

- If A+C is even, the answer is \frac{A+C}{2}
- Otherwise, the answer is -1.

# TIME COMPLEXITY:

\mathcal{O}(1) per testcase.

# CODE:

## Editorialist's code (Python)

```
for _ in range(int(input())):
a, c = map(int, input().split())
print((a+c)//2 if a%2 == c%2 else -1)
```