Problem A
ATM Maintenance

You are a maintenance worker for a large bank that recently bought new ATMs. All of them are working flawlessly, except for a stubborn one on Main Street. It seems to have a limited amount of money left in the machine, but the system reporting this number is not working properly. To find out for sure, you set some volunteers out to try and fix the problem by having them attempt to withdraw money from their accounts and see if it works.

Initially, the ATM contains a total of $K$ units of money. $N$ people (numbered $1$ through $N$) want to withdraw money.

The people come in and try to withdraw money one by one, in order. Whenever someone tries to withdraw money, if the machine has at least the required amount of money, it will give out the required amount. Otherwise, it will throw an error and not give out anything; in that case, this person will return home directly without trying to do anything else.

For each person, determine whether they will get the required amount of money or not.

Input

The first line of the input contains two space-separated integers $N$ ($1 \le N \le 100$) and $K$ ($1 \le K \le 100\, 000$). The second line contains $N$ space-separated integers $A_1,A_2,\ldots ,A_ N$ ($0 \le A_ i \le 10\, 000$), corresponding to the amount of money each person withdraws.

Output

Output a single line containing a string with length $N$. For each person, the i-th character of this string should be $1$ if the i-th person will successfully withdraw their money or $0$ otherwise.

5 10
3 5 3 2 1

11010