## Shopping Mall Design

Points: 1
Time limit: 1.0s
Memory limit: 256M

Author:
Problem types

Antoni is designing a new shopping mall! It is comprised of $$n$$ cells numbered from $$1$$ to $$n$$ in a line. Of course, customers want to visit many different stores.

So, Matt has designed a transportation system to move people between the shops.

He thought of $$n-1$$ positive integers $$a_1,...,a_n$$ where for every $$i (1 \leq i \leq n-1)$$ the condition $$1 \leq a_i \leq n-1$$ holds.

Then, he made $$n-1$$ tunnels numbered from $$1$$ to $$n-1$$. The $$i$$-th tunnel connects shop $$i$$ and shop $$(i+a_i)$$. To keep the 'flow' of the shopping mall, constant one cannot travel backwards through a tunnel, only forwards. Trivially, since $$1 \leq a_i \leq n-1$$ one cannot leave the mall once entering, genius!

At this point I should reveal I am stuck in this forsaken mall at cell $$1$$ and want to go to cell $$t$$ (they're having a really good sale). However, I don't know if I can get there, can you help me determine if I can reach cell $$t$$ using the tunnel system?

#### Input Specification

Two lines. The first line contains two space-separated integers $$n (3 \leq n \leq 3 \times 10^4)$$ and $$t (2\leq t \leq n)$$; the number of shops and the index of the shop I want to get to.

The second line contains $$n-1$$ space-separated integers $$a_1,...,a_{n-1} (1\leq a_i \leq n-1)$$.

One is also guaranteed that using the tunnels, it is impossible to leave the shopping mall.

#### Output Specification

If I can get to the shop $$t$$ using the tunnels print "YES". Otherwise, print "NO".

#### Sample Input 1

6 4
1 2 1 2 1 2

#### Sample Output 1

YES

#### Sample Input 2

8 5
1 2 1 2 1 1 1

#### Sample Output 2

NO

#### Note

In the first example, we visit the shops $$1,2,4$$; so we can reach shop $$4$$.

In the second example, we can only visit shops $$1,2,4,6,7,8$$; so wee cannot visit shop $$5$$.