human
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.

Input

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

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

Output

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.

Examples

Input

3 11
2 3 1 2 2 2 3 2 2 3 1

Output

00100000001

Input

4 8
4 1 3 3 2 3 3 3

Output

00001000

Note

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.
Using python3 can you solve the prior task?

What is a Python code to determine whether Arkady held the round right after creating this problem, or not?
assistant
#Here is Python code to determine whether Arkady held the round right after creating this problem, or not.

#      
import collections, atexit, math, sys, bisect 

sys.setrecursionlimit(1000000)
def getIntList():
    return list(map(int, input().split()))    

try :
    #raise ModuleNotFoundError
    import numpy
    def dprint(*args, **kwargs):
        #print(*args, **kwargs, file=sys.stderr)
        # in python 3.4 **kwargs is invalid???
        print(*args,  file=sys.stderr)
    dprint('debug mode')
except Exception:
    def dprint(*args, **kwargs):
        pass


inId = 0
outId = 0
if inId>0:
    dprint('use input', inId)
    sys.stdin = open('input'+ str(inId) + '.txt', 'r') #标准输出重定向至文件
if outId>0:
    dprint('use output', outId)
    sys.stdout = open('stdout'+ str(outId) + '.txt', 'w') #标准输出重定向至文件
    atexit.register(lambda :sys.stdout.close())     #idle 中不会执行 atexit
    
N, M = getIntList()

za = getIntList()
cnt = [ 0 for i in range(111000) ]
ext = cnt.copy()
for x in za:
    cnt[x] +=1
    ext[cnt[x]] +=1
    if ext[cnt[x]] ==N:
        print(1,end = '')
    else:
        print(0,end = '')