Uolevi is playing with chess pieces. He thinks that rooks are too strong and has decided to make them weaker. Now a rook can only move up or down. Additionally, the rook can only move in certain step lengths. Uolevi has written down a list of possible step lengths, which consists of n positive integers. Formally, after each step, the y-coordinate of the rook is increased or decreased by a number a_i that is included in the list.

Now Uolevi wants to test how bad the rook is. He wonders if it can capture a stationary pawn y squares in front of it in an infinitely large board after a finite number of moves.

Input

The first line contains two integers n and y. The second line contains n integers a_1,\,a_2,\dots,\,a_n.

Output

Print "Yes" if the rook can capture the pawn and "No" otherwise.

Constraints

• 1 \leq n \leq 10^5
• 1 \leq y \leq 10^9
• 1 \leq a_i \leq 10^9

Example 1

Input:

3 6
8 14 4

Output:

Yes

Example 2

Input:

1 1
2

Output:

No