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 is given from Standard Input in the following format:

```
$N$ $X$
$A_1$ $A_2$ $\ldots$ $A_N$
```

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

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

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.

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.