B'Igor had a sequence d_1, d_2, ... , d_n of integers. When Igor entered the classroom there was an integer x written on the blackboard. Igor generated sequence p using the following algorithm: For example, if x = 3 , and d = [1, -1, 2] , p will be equal [3, 4, 3, 4, 5] . Igor decided to calculate the length of the longest increasing subsequence of p and the number of them. A sequence a is a subsequence of a sequence b if a can be obtained from b by deletion of several (possibly, zero or all) elements. A sequence a is an increasing sequence if each element of a (except the first one) is strictly greater than the previous element. For p = [3, 4, 3, 4, 5] , the length of longest increasing subsequence is 3 and there are 3 of them: [ underline{3}, underline{4}, 3, 4, underline{5}] , [ underline{3}, 4, 3, underline{4}, underline{5}] , [3, 4, underline{3}, underline{4}, underline{5}] . The first line contains a single integer n ( 1 <= q n <= q 50 ) -- the length of the sequence d . The second line contains a single integer x ( -10^9 <= q x <= q 10^9 ) -- the integer on the blackboard. The third line contains n integers d_1, d_2, ldots, d_n ( -10^9 <= q d_i <= q 10^9 ). Print two integers: You should print only the second number modulo 998244353 . The first test case was explained in the statement. In the second test case p = [100, 101, 102, 103, 104, 105, 104, 103, 102, 103, 104, 105, 106, 107, 108] . In the third test case p = [1, 2, ldots, 2000000000] . '...