You know combinations: for example, 
if you take 5 cards from a 52 cards deck you have 2,598,960 different combinations.
In mathematics the number of x combinations you can take from a set of n elements
is called the binomial coefficient of n and x, or more often `n choose x`.
The formula to compute `m = n choose x` is: `m = n! / (x! * (n - x)!)`
where ! is the factorial operator.
You are a renowned poster designer and painter. You are asked to provide 6 posters 
all having the same design each in 2 colors. Posters must all have a different color combination and you have the choice of 4 colors: red, blue, yellow, green. 
How many colors can you choose for each poster?
The answer is two since `4 choose 2 = 6`. The combinations will be:
{red, blue}, {red, yellow}, {red, green}, {blue, yellow}, {blue, green}, {yellow, green}.
Now same question but you have 35 posters to provide and 7 colors available. How many colors for each poster?
If you take combinations `7 choose 2` you will get 21 with the above formula.
But 21 schemes aren't enough for 35 posters. If you take `7 choose 5` combinations you will get 21 too.
Fortunately if you take `7 choose 3` or `7 choose 4` combinations you get 35 and so each poster will have a different combination of
3 colors or 5 colors. You will take 3 colors because it's less expensive.
Hence the problem is: 
knowing `m` (number of posters to design), 
knowing `n` (total number of available colors), 
let us 
search `x` (number of colors for each poster so that each poster has a unique combination of colors and the number of combinations is exactly the same as the number of posters).
In other words we must find **x** such as `n choose x = m (1)` for a given m and a given n;
`m >= 0 and n > 0`. If many x are solutions give as result the smallest x.
It can happen that when m is given at random there are no x satisfying `equation (1)` then
return -1.
Examples:
```
checkchoose(6, 4) --> 2
checkchoose(4, 4) --> 1
checkchoose(4, 2) --> -1
checkchoose(35, 7) --> 3
checkchoose(36, 7) --> -1
a = 47129212243960
checkchoose(a, 50) --> 20
checkchoose(a + 1, 50) --> -1
```
from math import factorial as fact

def checkchoose(m, n):
    for k in range(0, (n)//2 + 1):
        if fact(n) // (fact(n-k) * fact(k)) == m:
            return k
    return -1
from math import factorial as fact

def checkchoose(m, n):
    for k in range(0, (n)//2 + 1):
        if fact(n) // (fact(n-k) * fact(k)) == m:
            return k
    return -1