B"For an array c of nonnegative integers, MEX(c) denotes the smallest nonnegative integer that doesn't appear in it. For example, MEX([0, 1, 3]) = 2 , MEX([42]) = 0 . You are given integers n, k , and an array [b_1, b_2, ldots, b_n] . Find the number of arrays [a_1, a_2, ldots, a_n] , for which the following conditions hold: 0 <= a_i <= n for each i for each i from 1 to n . |MEX([a_1, a_2, ldots, a_i]) - b_i| <= k for each i from 1 to n . As this number can be very big, output it modulo 998 ,244 ,353 . The first line of the input contains two integers n, k ( 1 <= n <= 2000 , 0 <= k <= 50 ). The second line of the input contains n integers b_1, b_2, ldots, b_n ( -k <= b_i <= n+k ) -- elements of the array b . Output a single integer -- the number of arrays which satisfy the conditions from the statement, modulo 998 ,244 ,353 . "...