CF1188C Array Beauty

Let's call beauty of an array $ b_1, b_2, \ldots, b_n $ ( $ n > 1 $ ) — $ \min\limits_{1 \leq i < j \leq n} |b_i - b_j| $ . You're given an array $ a_1, a_2, \ldots a_n $ and a number $ k $ . Calculate the sum of beauty over all subsequences of the array of length exactly $ k $ . As this number can be very large, output it modulo $ 998244353 $ . A sequence $ a $ is a subsequence of an array $ b $ if $ a $ can be obtained from $ b $ by deletion of several (possibly, zero or all) elements.

N/A

N/A

In the first example, there are $ 4 $ subsequences of length $ 3 $ — $ [1, 7, 3] $ , $ [1, 3, 5] $ , $ [7, 3, 5] $ , $ [1, 7, 5] $ , each of which has beauty $ 2 $ , so answer is $ 8 $ . In the second example, there is only one subsequence of length $ 5 $ — the whole array, which has the beauty equal to $ |10-1| = 9 $ .