Contest Duration: - (local time) (100 minutes) Back to Home
D - Robot Arms 2 /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• p_1 = (0, 0)
• p_2 = (A_1, 0)
• p_{N+1} = (x, y)
• p_i と点 p_{i+1} の距離は A_i (1 \leq i \leq N)
• 線分 p_i p_{i+1} と線分 p_{i+1} p_{i+2} のなす角は 90 度 (1 \leq i \leq N - 1)

### 制約

• 2 \leq N \leq 10^3
• 1 \leq A_i \leq 10
• |x|, |y| \leq 10^4
• 入力される値はすべて整数

### 入力

N x y
A_1 A_2 \dots A_N


### 入力例 1

3 -1 1
2 1 3


### 出力例 1

Yes


xy 座標平面に p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 1), p_4 = (-1, 1) として点を配置したのが以下の図です。これは問題文の条件をすべて満たしています。

### 入力例 2

5 2 0
2 2 2 2 2


### 出力例 2

Yes


p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 2), p_4 = (0, 2), p_5 = (0, 0), p_6 = (2, 0) とすれば問題文の条件をすべて満たすことができます。同じ座標に複数の点を置いてもよいのに注意してください。

### 入力例 3

4 5 5
1 2 3 4


### 出力例 3

No


### 入力例 4

3 2 7
2 7 4


### 出力例 4

No


### 入力例 5

10 8 -7
6 10 4 1 5 9 8 6 5 1


### 出力例 5

Yes


Score : 400 points

### Problem Statement

You are given a sequence A = (A_1, A_2, \dots, A_N) of length N consisting of positive integers, and integers x and y.
Determine whether it is possible to place N+1 points p_1, p_2, \dots, p_N, p_{N+1} in the xy-coordinate plane to satisfy all of the following conditions. (It is allowed to place two or more points at the same coordinates.)

• p_1 = (0, 0).
• p_2 = (A_1, 0).
• p_{N+1} = (x, y).
• The distance between the points p_i and p_{i+1} is A_i. (1 \leq i \leq N)
• The segments p_i p_{i+1} and p_{i+1} p_{i+2} form a 90 degree angle. (1 \leq i \leq N - 1)

### Constraints

• 2 \leq N \leq 10^3
• 1 \leq A_i \leq 10
• |x|, |y| \leq 10^4
• All values in the input are integers.

### Input

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

N x y
A_1 A_2 \dots A_N


### Output

If it is possible to place p_1, p_2, \dots, p_N, p_{N+1} to satisfy all of the conditions in the Problem Statement, print Yes; otherwise, print No.

### Sample Input 1

3 -1 1
2 1 3


### Sample Output 1

Yes


The figure below shows a placement where p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 1), and p_4 = (-1, 1). All conditions in the Problem Statement are satisfied.

### Sample Input 2

5 2 0
2 2 2 2 2


### Sample Output 2

Yes


Letting p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 2), p_4 = (0, 2), p_5 = (0, 0), and p_6 = (2, 0) satisfies all the conditions. Note that multiple points may be placed at the same coordinates.

### Sample Input 3

4 5 5
1 2 3 4


### Sample Output 3

No


### Sample Input 4

3 2 7
2 7 4


### Sample Output 4

No


### Sample Input 5

10 8 -7
6 10 4 1 5 9 8 6 5 1


### Sample Output 5

Yes