Problem Statement

There are K robots on a number line. The $i-th robot (1 \leq i \leq K)$ is initially at the coordinate x_i.
The following procedure is going to take place exactly N times.

• Each robot chooses to move or not with probability $\frac{1}{2}$ each. The robots that move will simultaneously go the distance of 1 in the positive direction, and the other robots will remain still.

Here, all probabilistic decisions are independent.
Find the probability that no two robots meet, that is, there are never two or more robots at the same coordinate at the same time throughout the procedures, modulo 998244353 (see Notes).

Input

Input is given from Standard Input in the following format:
K N
$x_1 x_2 \ldots x_K$

Output

Print the answer.

Constraints

• $2 \leq K \leq 10$
• $1 \leq N \leq 1000$
• $0 \leq x_1 \lt x_2 \lt \cdots \lt x_K \leq 1000$
• All values in input are integers.

Sample Input 1

2 2
1 2

Sample Output 1

374341633

The probability in question is $\frac{5}{8}$.
We have $374341633 \times 8 \equiv 5\pmod{998244353}$, so you should print 374341633.

Sample Input 2

2 2
10 100

Sample Output 2

1

The probability in question may be 1.

Sample Input 3

10 832
73 160 221 340 447 574 720 742 782 970

Sample Output 3

553220346

见题面 Input 部分

见题面 Output 部分