Non-Adjacent Gift Boxes Selection

You are given a sequence of M gift boxes arranged in a line. Each box i (1 ≤ i ≤ M) contains a gift with a positive integer value A_i.

Your task is to determine whether there exists a subset of these boxes that can be selected such that:

• The sum of the values of the selected boxes is exactly V.
• No two selected boxes are adjacent (i.e. if box i is selected, then box i+1 cannot be selected).

In mathematical terms, if we define a binary indicator x_i with x_i = 1 when the i-th box is chosen and 0 otherwise, then the condition is to check if there exists a sequence {x₁, x₂, ..., x_M} satisfying:

$$\sum_{i=1}^{M} x_i \cdot A_i = V, \quad \text{and} \quad x_i + x_{i+1} \le 1 \quad \text{for all } 1 \le i < M. $$

You need to print Yes if such a selection exists, or No otherwise.

inputFormat

The input is given via stdin and follows the format below:

M V
A1 A2 ... AM

Where:

• M is the number of gift boxes.
• V is the target sum that needs to be achieved by selecting non-adjacent boxes.
• The second line contains M space-separated integers representing the values in the gift boxes.

outputFormat

The output should be printed to stdout and consists of a single line:

Yes

or

No

indicating whether a valid selection exists.

## sample

5 9
3 2 5 10 7

Yes