CF1100B.Build a Contest

Arkady coordinates rounds on some not really famous competitive programming platform. Each round features $n$ problems of distinct difficulty, the difficulties are numbered from $1$ to $n$.

To hold a round Arkady needs $n$ new (not used previously) problems, one for each difficulty. As for now, Arkady creates all the problems himself, but unfortunately, he can't just create a problem of a desired difficulty. Instead, when he creates a problem, he evaluates its difficulty from $1$ to $n$ and puts it into the problems pool.

At each moment when Arkady can choose a set of $n$ new problems of distinct difficulties from the pool, he holds a round with these problems and removes them from the pool. Arkady always creates one problem at a time, so if he can hold a round after creating a problem, he immediately does it.

You are given a sequence of problems' difficulties in the order Arkady created them. For each problem, determine whether Arkady held the round right after creating this problem, or not. Initially the problems pool is empty.

Arkady 在某个不太知名的编程竞赛平台上组织比赛。每场比赛包含 $n$ 道难度互不相同的题目，难度编号为 $1$ 到 $n$。

为了举办一场比赛，Arkady 需要 $n$ 道全新（此前未使用过）的题目，每道题对应一个唯一的难度（即难度 $1$ 至 $n$ 各一道）。目前，所有题目均由 Arkady 亲自出题；但遗憾的是，他无法直接创作指定难度的题目。相反，每当他创作一道题时，他会评估该题的难度（取值范围为 $1$ 到 $n$），并将该题加入题库。

在任意时刻，只要 Arkady 能从题库中选出 $n$ 道全新且难度互不相同（即恰好覆盖难度 $1, 2, \dots, n$）的题目，他便会立即用这些题目举办一场比赛，并将这 $n$ 道题从题库中移除。Arkady 每次只创作一道题；因此，若他在创作完某道题后满足办赛条件，便会立即举办一场比赛。

现给出 Arkady 创作题目的难度序列（按创作顺序排列）。对每一道题，请判断 Arkady 是否在创作完该题后立即举办了一场比赛。初始时题库为空。

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 10^5$) — the number of difficulty levels and the number of problems Arkady created.

The second line contains $m$ integers $a_1, a_2, \ldots, a_m$ ($1 \le a_i \le n$) — the problems' difficulties in the order Arkady created them.

第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 10^5$）—— 分别表示难度等级的数量和 Arkady 创建的问题数量。

第二行包含 $m$ 个整数 $a_1, a_2, \ldots, a_m$（$1 \le a_i \le n$）—— 表示 Arkady 按创建顺序给出的问题难度。

Print a line containing $m$ digits. The $i$-th digit should be $1$ if Arkady held the round after creation of the $i$-th problem, and $0$ otherwise.

输出一行包含 $m$ 个数字的字符串。其中第 $i$ 个数字应为 $1$，当且仅当 Arkady 在第 $i$ 个题目创建之后举办了该场比赛；否则为 $0$。

In the first example Arkady held the round after the first three problems, because they are of distinct difficulties, and then only after the last problem.

在第一个例子中，阿尔卡季在前三个题目之后举办了比赛，因为这三个题目的难度各不相同；然后仅在最后一道题目之后再次举办比赛。