The accounts of the "Fat to Fit Club (FFC)" association are supervised by John as a volunteered accountant.
The association is funded through financial donations from generous benefactors. John has a list of
the first `n` donations: `[14, 30, 5, 7, 9, 11, 15]`
He wants to know how much the next benefactor should give to the association so that the 
average of the first `n + 1` donations should reach an average of `30`.
After doing the math he found `149`. He thinks that he made a mistake.
Could you help him?

if `dons = [14, 30, 5, 7, 9, 11, 15]` then `new_avg(dons, 30) --> 149`

The function `new_avg(arr, navg)` should return the expected donation
(rounded up to the next integer) that will permit to reach the average `navg`. 

Should the last donation be a non positive number `(<= 0)` John wants us to throw (or raise) an error or

- return Nothing in Haskell
- return None in F#, Ocaml, Scala
- return `-1` in C, Fortran,  Nim, PowerShell, Go, Prolog
- echo `ERROR` in Shell
- raise-argument-error in Racket

so that he clearly sees that his expectations are not great enough.

Notes: 

- all donations and `navg` are numbers (integers or floats), `arr` can be empty.
- See examples below and "Test Samples" to see which return is to be done.

```
new_avg([14, 30, 5, 7, 9, 11, 15], 92) should return 645
new_avg([14, 30, 5, 7, 9, 11, 15], 2) 
should raise an error (ValueError or invalid_argument or argument-error or DomainError) 
or return `-1` or ERROR or Nothing or None depending on the language.
```

Difficulty: introductory

Starter code:

def new_avg(arr, newavg):
	

Solutions:
from math import ceil


def new_avg(arr, newavg):
    value = int(ceil((len(arr)+1) * newavg - sum(arr)))
    if value < 0:
        raise ValueError
    
    return value

def new_avg(arr, newavg):
    extra = newavg*float(len(arr) + 1) - sum(arr)
    if extra < 0:
        raise ValueError
    return int(extra + 0.999)

import math
def new_avg(arr, newavg):
    result =  math.ceil(newavg*(len(arr)+1)-sum(arr))    
    if result <= 0:
        raise ValueError('error')
    else:
        return result

from math import ceil

def new_avg(arr, newavg):
    # calculate the required amount
    required = ceil(newavg * (len(arr) + 1) - sum(arr))
    # throw an error if non-positive
    assert required > 0
    # otherwise return result
    return required

from math import ceil


def new_avg(arr, average):
    nums_sum = total_nums = 0
    for a in arr:
        nums_sum += a
        total_nums += 1
    donation = ceil((average * (total_nums + 1)) - nums_sum)
    if donation > 0:
        return donation
    raise ValueError


from math import *
def new_avg(arr, newavg):
    v = ceil(newavg*(len(arr)+1) - sum(arr))
    if v >= 0:
        return v
    else:
        raise ValueError


from math import ceil

def new_avg(lst, newavg):
    nxt = newavg * (len(lst) + 1) - sum(lst)
    if nxt <= 0:
        raise ValueError
    return ceil(nxt)

import math
def new_avg(arr, newavg):
    a = math.ceil(newavg * (len(arr) + 1) - sum(arr))
    if a > 0:
        return(a)
    return Error

import math
def new_avg(arr, newavg):
    new_donation = newavg*(len(arr)+1)-sum(arr)
    if new_donation <= 0: raise("Error")
    return math.ceil(new_donation)

def new_avg(arr, newavg):
    value = round(len(arr) * newavg - ( sum(arr)-newavg ) + .49 )
    
    if value < 0:
        raise ValueError("Error expected")
    return value