K-summary

An unknown array $x$ holds $N$ integers. The $K$-summary of that array is what you get by cutting the array into segments of length $K$ from the front and adding up the elements of each segment. If $N$ is not divisible by $K$, the last segment is shorter than $K$.

In other words, the elements of the $K$-summary are, in order, $x[1] + \cdots + x[K]$, $x[K+1] + \cdots + x[2K]$, and so on, and only the last sum, the one that contains $x[N]$, can have fewer than $K$ terms. For example, the 5-summary of an array of 13 elements has three elements: the sum of elements 1 to 5, the sum of elements 6 to 10, and the sum of elements 11 to 13.

One $K$-summary alone is not enough to recover the elements of the original array. If you know the summaries for several different values of $K$, some elements are pinned down to a single value. You are given the length $N$ and the numbers $K_1, K_2, \ldots, K_M$. Write a program that computes how many elements of the original array are uniquely determined when all $K_i$-summaries are known. That count does not depend on the values written in the summaries.

The first line contains the array length $N$ and the number of summaries $M$. ($3 \le N \le 10^9$, $1 \le M \le 10$)

The second line contains distinct integers $K_1, K_2, \ldots, K_M$. ($2 \le K_i < N$)

Print the number of elements that are uniquely determined.

In the first example, only $x[3]$ can be determined.

In the second example, $x[3]$ and $x[4]$ can be determined.