# Task
 When a candle finishes burning it leaves a leftover. makeNew leftovers can be combined to make a new candle, which, when burning down, will in turn leave another leftover.

 You have candlesNumber candles in your possession. What's the total number of candles you can burn, assuming that you create new candles as soon as you have enough leftovers?

# Example

 For candlesNumber = 5 and makeNew = 2, the output should be `9`.

 Here is what you can do to burn 9 candles:
```
burn 5 candles, obtain 5 leftovers;
create 2 more candles, using 4 leftovers (1 leftover remains);
burn 2 candles, end up with 3 leftovers;
create another candle using 2 leftovers (1 leftover remains);
burn the created candle, which gives another leftover (2 leftovers in total);
create a candle from the remaining leftovers;
burn the last candle.
Thus, you can burn 5 + 2 + 1 + 1 = 9 candles, which is the answer.
```

# Input/Output


 - `[input]` integer `candlesNumber`

    The number of candles you have in your possession.

    Constraints: 1 ≤ candlesNumber ≤ 50.
    

 - `[input]` integer `makeNew`

    The number of leftovers that you can use up to create a new candle.

    Constraints: 2 ≤ makeNew ≤ 5.
    

 - `[output]` an integer

Difficulty: introductory

Starter code:

def candles(m, n):
	

Solutions:
def candles(candles, make_new):
    return candles + (candles - 1) // (make_new - 1)

def candles(m, n):
    burn = leftover = 0
    while m:
        burn += m
        m, leftover = divmod(leftover + m, n)
    return burn

def candles(a, b):
    return a + (a - 1) // (b - 1)

from functools import lru_cache

@lru_cache(maxsize=None)
def candles(m, n, l=0):
    if not m and l < n: return 0
    m, l = m+l//n, l%n
    return m + candles(0, n, l+m)

def candles(m, n):
    c, r = m, 0
    while m:
        m, r = divmod(m+r, n)
        c += m
    return c


def candles(m, n):
    c = m
    while m >= n:
        a, b = divmod(m, n)
        c += a
        m = a + b
    return c

def candles(m, n):
    answer = 0
    candles, leftovers = m, 0
    while candles >= 1 or leftovers >= n:
        answer += candles
        leftovers += candles
        candles = leftovers//n
        leftovers -= leftovers//n*n
    return answer

def candles(candles1, leftovers):
    return candlesop(candles1, leftovers)


# Candle operations.
def candlesop(candles1, leftovers):
    candle1 = candles1
    answer = 0
    left = 0
    # while loop; as long as some candles remain, the loop keeps running.
    while candle1 != 0:
        answer += candle1
        left += candle1
        candle1 = left // leftovers
        left = left % leftovers
    return answer

def candles(m,n):
    total=0
    l=0
    while m:
        total+=m
        m,l=divmod(m+l,n)
    return total

def candles(m, n):
    burnt = m
    leftovers = m
    while leftovers//n >= 1:
        burnt += leftovers//n
        leftovers = leftovers%n + leftovers//n
    return burnt