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Statement

There are $N$ balls numbered $1$ to $N$. Ball $i$ has an integer $A_i$ written on it.

For a way of choosing some balls from the $N$ balls, define the score of that choice as the square of the sum of the numbers written on the chosen balls.

Find the sum, modulo $998244353$, of the scores of all $\binom{N}{K}$ ways of choosing $K$ balls from the $N$ balls.

Input

The input is given from Standard Input in the following format:

• $N$ $K$
• $A_1$ $A_2$ $\dots$ $A_N$

Output

Output the answer.

Constraints

• $1 \leq K \leq N \leq 2\times 10^5$
• $1 \leq A_i \leq 10^9$
• All input values are integers.

3 2
1 10 100

22422

There are three ways of choosing two balls from three balls: choosing balls $1,2$ gives a score of $(1+10)^2=121$, choosing balls $1,3$ gives a score of $(1+100)^2=10201$, and choosing balls $2,3$ gives a score of $(10+100)^2=12100$.

The answer is the sum of these, $121+10201+12100=22422$.

5 2
10 10 20 20 20

10600

Multiple balls may have the same number written on them.

2 1
998244353 998244353

0

Find the sum modulo $998244353$.

• 来源：AtCoder ABC 471 E