Ghosts In The Robots

Do you still remember the movie "I, robot" ? In that movie, Sunny is a very special, unique robot who can dream! As we known, robot is a machine installed with artificial intelligence, and it can't response to the situations which are not contained in the pre-designed programs. But the creator of Sunny detects that the logic sequences existed in the robot would change under some particular cases, e.g. magnetic field, noises etc. He called this unpredictable sequence ghosts in the robot because these random combination of 1s and 0 s could yield unpredictable behaviors of robots, it was terrible! In order to detect this situation as soon as possible, you should help the prof. via your outstanding programming skills.
You would be given a sequence with the length of N, and this sequence is only contained 0 and 1.Based on the professor's recent research data, the sequence could have at most F successive bits flipped(that means 0 changes to 1, and 1 changes to 0) and could have at most R successive bits remained the same. Based on these situations, you should calculate the maximum number of 1 in the sequence after those changes.

The input would have multiple test cases, each test case has two lines, The first line contains two integer R and F(1 <= R <= 50, 1 <= F <= 50), indicating the number of the digits remain the same and the number of the digits flipped respectively. the second line is a sequence only comprises of 0 and 1, whose length is between 1 and 1000.The input would end when R == 0 and F == 0.

For each case, print a line with the maximum number of 1 left in the sequence.

4 1
1111
2 2
1111
0 0

4
3

Hint
For test case 2, one change is like this:
1 1 1 1
Remain Flip Remain Remain
So the answer is 3

HDU 8th Programming Contest Site（2）