Card Drawing

Bob likes drawing cards.

Bob recently started playing a card game called "Lord Connection". There are $n$ different characters in the game, numbered $1 \sim n$. When Bob obtains $k$ cards with consecutive numbers, he can form the theoretically strongest lineup.

There are $m$ different cards in the current card pool. Each time Bob draws a card, he has an equal probability of obtaining any card from the pool. If Bob draws a card he already possesses, nothing happens, and the draw opportunity is wasted. Bob is a cautious person, and he wants to know the expected number of draws required to stop drawing once he has obtained $k$ cards with consecutive numbers.

Input

The first line contains two integers $m, k$.

The second line contains $m$ distinct integers $a_1, a_2, \dots, a_m$, representing the characters available in the card pool.

The value $n$ in the problem statement is the maximum value among $a_i$.

Output

Output a single integer representing the expected number of draws modulo $p = 998244353$. That is, if the expected value is represented as an irreducible fraction $\frac{a}{b}$, you need to output an integer $c$ such that $c \times b \equiv a \pmod{p}$.

Examples

Input 1

3 2
1 2 3

Output 1

499122180

Note 1

If the first card drawn is card 2, the expected number of draws is $1 + \frac{3}{2}$; if the first card drawn is card 1 or card 3, the expected number of draws is $1 + 3$. Therefore, the answer is $\frac{1}{3}(1 + \frac{3}{2}) + \frac{2}{3}(1 + 3) = 3.5$.

Input 2

10 2
1 2 3 4 5 7 8 9 11 12

Output 2

839792873

Constraints

• For the first 10% of data, $m \le 10$.
• For another 10% of data, $m \le 500$ and $k = m - 1$.
• For another 10% of data, $m \le 500$ and it is guaranteed that there is exactly one theoretically strongest lineup.
• For another 10% of data, $m \le 500$ and it is guaranteed that any two possible theoretically strongest lineups are disjoint.
• For the first 50% of data, $m \le 500$.
• For the first 70% of data, $m \le 5000$.
• For another 10% of data, $k = 5$.
• For another 10% of data, $k = 2000$.
• For 100% of data, $1 \le m \le 200000$, $1 \le a_i \le 2m$, $2 \le k \le m$. It is guaranteed that there is at least one theoretically strongest lineup (i.e., $k$ cards with consecutive numbers) that can be drawn from the pool.