Valera and Fools

题目描述

One fine morning, $ n $ fools lined up in a row. After that, they numbered each other with numbers from $ 1 $ to $ n $ , inclusive. Each fool got a unique number. The fools decided not to change their numbers before the end of the fun. Every fool has exactly $ k $ bullets and a pistol. In addition, the fool number $ i $ has probability of $ p_{i} $ (in percent) that he kills the fool he shoots at. The fools decided to have several rounds of the fun. Each round of the fun looks like this: each currently living fool shoots at another living fool with the smallest number (a fool is not stupid enough to shoot at himself). All shots of the round are perfomed at one time (simultaneously). If there is exactly one living fool, he does not shoot. Let's define a situation as the set of numbers of all the living fools at the some time. We say that a situation is possible if for some integer number $ j $ ( $ 0<=j<=k $ ) there is a nonzero probability that after $ j $ rounds of the fun this situation will occur. Valera knows numbers $ p_{1},p_{2},...,p_{n} $ and $ k $ . Help Valera determine the number of distinct possible situations.

输入输出格式

输入格式

The first line contains two integers $ n,k $ ( $ 1<=n,k<=3000 $ ) — the initial number of fools and the number of bullets for each fool. The second line contains $ n $ integers $ p_{1},p_{2},...,p_{n} $ ( $ 0<=p_{i}<=100 $ ) — the given probabilities (in percent).

输出格式

Print a single number — the answer to the problem.

输入输出样例

输入样例 #1

3 3
50 50 50

输出样例 #1

7

输入样例 #2

1 1
100

输出样例 #2

1

输入样例 #3

2 1
100 100

输出样例 #3

2

输入样例 #4

3 3
0 0 0

输出样例 #4

1

说明

In the first sample, any situation is possible, except for situation $ {1,2} $ . In the second sample there is exactly one fool, so he does not make shots. In the third sample the possible situations are $ {1,2} $ (after zero rounds) and the "empty" situation $ {} $ (after one round). In the fourth sample, the only possible situation is $ {1,2,3} $ .