Home

Contest: Task: Related: TaskA TaskC

Score : $200$ points

Problem Statement

Takahashi has $N$ foods in his house. The $i$-th food has the tastiness of $A_i$.
He dislikes $K$ of these foods: for each $i=1,2,\ldots,K$, he dislikes the $B_i$-th food.

Out of the foods with the greatest tastiness among the $N$ foods, Takahashi will randomly choose one and eat it.
If he has a chance to eat something he dislikes, print Yes; otherwise, print No.

Constraints

  • $1\leq K\leq N\leq 100$
  • $1\leq A_i\leq 100$
  • $1\leq B_i\leq N$
  • All $B_i$ are distinct.
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$
$A_1$ $A_2$ $\ldots$ $A_N$
$B_1$ $B_2$ $\ldots$ $B_K$

Output

If Takahashi has a chance to eat a food he dislikes, print Yes; otherwise, print No.

Sample Input 1

5 3
6 8 10 7 10
2 3 4

Sample Output 1

Yes

Among the five foods, the ones with the greatest tastiness are Food $3$ and $5$, of which he eats one.
He dislikes Food $2$, $3$, and $4$, one of which he has a chance to eat: Food $3$.
Therefore, the answer is Yes.

Sample Input 2

5 2
100 100 100 1 1
5 4

Sample Output 2

No

The foods with the greatest tastiness are Food $1$, $2$, and $3$, none of which he has a chance to eat.

Sample Input 3

2 1
100 1
2

Sample Output 3

No

The food with the greatest tastiness is Food $1$, which he has no chance to eat.