'''Task description
Write a function:

def solution(A, B, K)

that, given three integers A, B and K, returns the number of integers within the range [A..B] that are divisible by K, i.e.:

{ i : A ≤ i ≤ B, i mod K = 0 }

For example, for A = 6, B = 11 and K = 2, your function should return 3, because there are three numbers divisible by 2 within the range [6..11], namely 6, 8 and 10.

Write an efficient algorithm for the following assumptions:

A and B are integers within the range [0..2,000,000,000];
K is an integer within the range [1..2,000,000,000];
A ≤ B.'''

# https://app.codility.com/demo/results/trainingSESF82-TQ5/

# own solution
def solution(A, B, K):
    while A % K:
        A += 1     
    if not B % K:
        return len(range(A, B + K, K))
    else:
        return len(range(A, B, K))


# mathematical one
def solution(A, B, K):
    if A % K == 0:
        return (B - A) // K + 1
    else:
        return (B - (A - A % K )) // K

