Score : $200$ points

问题描述

高桥商店销售 $N$ 种产品。第 $i$ 个产品的常规价格是 $A_i$ 日元（日本货币）。

今天商店举行特价促销，对于第 $2$、$4$ 项以及随后所有偶数序号的产品，每件优惠 $1$ 日元。而第 $1$、$3$ 项以及随后所有奇数序号的产品按原价销售。

你现在拥有 $X$ 日元。请问，你能否用这些钱购买全部 $N$ 种产品呢？

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 09:22:29