#916 Two Printers

Statement

Statement language

There are two printers, A and B. Each printer contains $N$ cards. In each printer, the numbers from $1$ to $N$ appear exactly once.

Let $A_1,A_2,\cdots,A_N$ be the cards in printer A from front to back, and let be the cards in printer B from front to back.

You perform exactly $2N$ operations to print all cards. In one operation, choose a printer that still has at least one card, print its front card, and remove that card.

The first operation causes no switch. Starting from the second operation, the number of switches increases by $1$ whenever the chosen printer differs from the printer used in the previous operation.

After all operations, the $2N$ printed numbers form an output sequence in order. The same output sequence may be produced by more than one sequence of operations.

Count the distinct output sequences that can be produced by an operation sequence using at most $K$ switches. If several operation sequences produce the same output sequence, count that output sequence once as long as at least one of them uses at most $K$ switches.

Print the answer modulo $998\,244\,353$ .

Input

The input is given in the following format.

$N\ K$ $A_1\ A_2\ \cdots\ A_N$

Output

Print the number of distinct output sequences satisfying the condition, modulo $998\,244\,353$ .

Constraints

$1 \le N \le 300$ .
$0 \le K \le 2N-1$ .
is a permutation of .

Samples

Sample 1

Input

1 0
1
1

Output

0

Printing all cards requires using both printers and hence at least one switch. Since $K=0$ , no output sequence is possible.

Sample 2

Input

1 1
1
1

Output

1

Using A then B, or B then A, requires one switch. Both methods produce $(1,1)$ , so this sequence is counted once.

Sample 3

Input

2
2
1

Output

4

The four possible output sequences are , , , and . They can be produced using printers in the orders AABB, ABBA, BAAB, and BBAA, respectively, with switches.