New Year Transportation

题意翻译

 感谢@wmxwmx 提供的翻译

题目描述

New Year is coming in Line World! In this world, there are $ n $ cells numbered by integers from $ 1 $ to $ n $ , as a $ 1×n $ board. People live in cells. However, it was hard to move between distinct cells, because of the difficulty of escaping the cell. People wanted to meet people who live in other cells. So, user tncks0121 has made a transportation system to move between these cells, to celebrate the New Year. First, he thought of $ n-1 $ positive integers $ a_{1},a_{2},...,a_{n-1} $ . For every integer $ i $ where $ 1<=i<=n-1 $ the condition $ 1<=a_{i}<=n-i $ holds. Next, he made $ n-1 $ portals, numbered by integers from 1 to $ n-1 $ . The $ i $ -th ( $ 1<=i<=n-1 $ ) portal connects cell $ i $ and cell $ (i+a_{i}) $ , and one can travel from cell $ i $ to cell $ (i+a_{i}) $ using the $ i $ -th portal. Unfortunately, one cannot use the portal backwards, which means one cannot move from cell $ (i+a_{i}) $ to cell $ i $ using the $ i $ -th portal. It is easy to see that because of condition $ 1<=a_{i}<=n-i $ one can't leave the Line World using portals. Currently, I am standing at cell $ 1 $ , and I want to go to cell $ t $ . However, I don't know whether it is possible to go there. Please determine whether I can go to cell $ t $ by only using the construted transportation system.

输入输出格式

输入格式

The first line contains two space-separated integers $ n $ ( $ 3<=n<=3×10^{4} $ ) and $ t $ ( $ 2<=t<=n $ ) — the number of cells, and the index of the cell which I want to go to. The second line contains $ n-1 $ space-separated integers $ a_{1},a_{2},...,a_{n-1} $ ( $ 1<=a_{i}<=n-i $ ). It is guaranteed, that using the given transportation system, one cannot leave the Line World.

输出格式

If I can go to cell $ t $ using the transportation system, print "YES". Otherwise, print "NO".

输入输出样例

输入样例 #1

8 4
1 2 1 2 1 2 1

输出样例 #1

YES

输入样例 #2

8 5
1 2 1 2 1 1 1

输出样例 #2

NO

说明

In the first sample, the visited cells are: $ 1,2,4 $ ; so we can successfully visit the cell $ 4 $ . In the second sample, the possible cells to visit are: $ 1,2,4,6,7,8 $ ; so we can't visit the cell $ 5 $ , which we want to visit.

题意翻译

 感谢@wmxwmx 提供的翻译