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?

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分