Problem Statement

AtCoder Inc. sells T-shirts with its logo.
You are given Takahashi's schedule for N days as a string S of length N consisting of 0, 1, and 2.
Specifically, for an integer $i satisfying 1\leq i\leq N$,

• if the i-th character of S is 0, he has no plan scheduled for the i-th day;
• if the i-th character of S is 1, he plans to go out for a meal on the i-th day;
• if the i-th character of S is 2, he plans to attend a competitive programming event on the i-th day.

Takahashi has M plain T-shirts, all washed and ready to wear just before the first day.
In addition, to be able to satisfy the following conditions, he will buy several AtCoder logo T-shirts.

• On days he goes out for a meal, he will wear a plain or logo T-shirt.
• On days he attends a competitive programming event, he will wear a logo T-shirt.
• On days with no plans, he will not wear any T-shirts. Also, he will wash all T-shirts worn at that point. He can wear them again from the next day onwards.
• Once he wears a T-shirt, he cannot wear it again until he washes it.

Determine the minimum number of T-shirts he needs to buy to be able to wear appropriate T-shirts on all scheduled days during the N days. If he does not need to buy new T-shirts, print 0.
Assume that the purchased T-shirts are also washed and ready to use just before the first day.

Input

The input is given from Standard Input in the following format:
N M
S

Output

Print the minimum number of T-shirts Takahashi needs to buy to be able to satisfy the conditions in the problem statement.
If he does not need to buy new T-shirts, print 0.

Constraints

• $1\leq M\leq N\leq 1000$
• S is a string of length N consisting of 0, 1, and 2.
• N and M are integers.

Sample Input 1

6 1
112022

Sample Output 1

2

If Takahashi buys two logo T-shirts, he can wear T-shirts as follows:

• On the first day, he wears a logo T-shirt to go out for a meal.
• On the second day, he wears a plain T-shirt to go out for a meal.
• On the third day, he wears a logo T-shirt to attend a competitive programming event.
• On the fourth day, he has no plans, so he washes all the worn T-shirts. This allows him to reuse the T-shirts worn on the first, second, and third days.
• On the fifth day, he wears a logo T-shirt to attend a competitive programming event.
• On the sixth day, he wears a logo T-shirt to attend a competitive programming event.

If he buys one or fewer logo T-shirts, he cannot use T-shirts to meet the conditions no matter what. Hence, print 2.

Sample Input 2

3 1
222

Sample Output 2

3

Sample Input 3

2 1
01

Sample Output 3

0

He does not need to buy new T-shirts.

见题面 Input 部分

见题面 Output 部分