Contest Duration: - (local time) (100 minutes) Back to Home
B - Can you buy them all? /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

あなたの所持金は X 円です。これら N 個の商品を全て買うことができますか？

### 制約

• 1 \leq N \leq 100
• 1 \leq X \leq 10000
• 1 \leq A_i \leq 100
• 入力は全て整数

### 入力

N X
A_1 A_2 \ldots A_N


### 出力

N 個の商品を全て買うことができるなら Yes、できないなら No と出力せよ。

### 入力例 1

2 3
1 3


### 出力例 1

Yes


1 番目の商品は 1 円、2 番目の商品は定価より 1 円引きの 2 円で買うことができます。あなたの所持金は 3 円なので、ちょうどの金額で 2 個の商品を全て買うことができます。

### 入力例 2

4 10
3 3 4 4


### 出力例 2

No


4 個の商品はそれぞれ 3 円、2 円、4 円、3 円で買うことができます。4 個の商品を全て買うためには 12 円必要ですが、あなたの所持金は 10 円なので全て買うことはできません。

### 入力例 3

8 30
3 1 4 1 5 9 2 6


### 出力例 3

Yes


Score : 200 points

### Problem Statement

Takahashi's shop sells N products. The usual price of the i-th product is A_i yen (Japanese currency).
It has a bargain sale today, with a discount of 1 yen off the usual prices for the 2-nd, 4-th, and the subsequent even-indexed products. The 1-st, 3-rd, and the subsequent odd-indexed products are sold for their usual prices.
You have X yen. Can you buy all the N products with this money?

### Constraints

• 1 \leq N \leq 100
• 1 \leq X \leq 10000
• 1 \leq A_i \leq 100
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N X
A_1 A_2 \ldots A_N


### Output

If you can buy all the N products, print Yes; otherwise, print No.

### Sample Input 1

2 3
1 3


### Sample Output 1

Yes


You can buy the 1-st product for 1 yen and the 2-nd product for 2 yen, 1 yen off the usual price. You have just enough money, 3 yen, to buy both of them.

### Sample Input 2

4 10
3 3 4 4


### Sample Output 2

No


You can buy these four products for 3 yen, 2 yen, 4 yen, and 3 yen, respectively. You need 12 yen to buy all of them, and since you have only 10 yen, you cannot buy all of them.

### Sample Input 3

8 30
3 1 4 1 5 9 2 6


### Sample Output 3

Yes