Calculate the values of counters after applying all alternating operations: increase counter by $1$; set value of all counters to current maximum.
You are given $N$ counters, initially set to $0$, and you have two possible operations on them:

• increase(X) − counter $X$ is increased by $1$,
• max counter − all counters are set to the maximum value of any counter.

A non-empty array $A$ is given. This array represents consecutive operations:

• if $A[K] = X$, such that $1 ≤ X ≤ N$, then operation $K$ is increase(X),
• if $A[K] = N + 1$ then operation $K$ is max counter.

For example, given integer $N = 5$ and array $A$ such that:

A[0] = 3 
A[1] = 4 
A[2] = 4 
A[3] = 6 
A[4] = 1 
A[5] = 4 
A[6] = 4

the values of the counters after each consecutive operation will be:

(0, 0, 1, 0, 0) 
(0, 0, 1, 1, 0) 
(0, 0, 1, 2, 0) 
(2, 2, 2, 2, 2) 
(3, 2, 2, 2, 2) 
(3, 2, 2, 3, 2) 
(3, 2, 2, 4, 2)

The goal is to calculate the value of every counter after all operations.

Write an efficient algorithm for the following assumptions:

• $N$ are integers within the range $[1..100,000]$;
• each element of array $A$ is an integer within the range $[1..N + 1]$.

returns a sequence of integers representing the values of the counters.