AT_abc471_e [ABC471E] Sum of Square of Sum

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.

The input is given from Standard Input in the following format: > $ N $ $ K $ $ A_1 $ $ \dots $ $ A_N $

Output the answer.

### Sample Explanation 1 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 $ . ### Sample Explanation 2 Multiple balls may have the same number written on them. ### Sample Explanation 3 Find the sum modulo $ 998244353 $ . ### Constraints - $ 1 \leq K \leq N \leq 2\times 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - All input values are integers.