### PROBLEM LINK:

**Author:** Hasan Jaddouh

**Tester:** Teja Vardhan Reddy

**Editorialist:** Hussain Kara Fallah

### DIFFICULTY:

Cakewalk

### PREREQUISITES:

NONE

### PROBLEM:

Chef had a sequence of **positive integers** with a length of N+K. He managed to calculate the arithmetic average of all elements of this sequence (an integer value let’s denote it by V), but then, his little brother deleted K elements from it. All deleted elements had the same value. Chef still knows the remaining N elements — a sequence A_1,A_2,…,A_N. Help him with restoring the original sequence by finding the value of the deleted elements or deciding that there is some mistake and the described scenario is impossible.

### Explanation:

Let’s denote the sum of the given N elements by S (S=A_1+A_2+A_3+...+A_N).

We know that the missing value ans occurred K times. So the sum of our original sequence is tot=S+K*ans. Also, the total number of elements of the original sequence is N+K. We have the mean average value of V.

V\,=\, \frac{S+K*ans}{N+K}

V*(N+K) = S+K*ans

V*(N+K) - S = K*ans

ans = \frac{V*(N+K) - S}{K}

Since the missing number is an integer that implies that K divides V*(N+K) - S

In other words (V*(N+K) - S) \, \, modulo\, K \equiv 0

In case the remainder of the division wasn’t 0 then there was some mistake and the answer is -1.

We concluded that ans = \frac{V*(N+K) - S}{K}. In some cases, we may have a negative answer (because the average given is less than the sum of given elements). Or it may be even 0 if the average was equal to the sum. In such cases, we must report that there’s some mistake as well because it’s stated that the sequence consisted of positive integers only.