E. Product Tuplestime limit per test8 secondsmemory limit per test128 megabytesinputstandard inputoutputstandard outputWhile roaming the mystic areas of Stonefalls, in order to drop legendary loot, an adventurer was given a quest as follows. He was given an array A = {a_1,a_2,...,a_N } of length N, and a number K.Define array B as B(q, A) =  { q-a_1, q-a_2, ..., q-a_N }. Define function F as F(B,K) being sum of products of all K-tuples of elements in array B. For example, if the array B is [2,3,4,5], and with K=3, sum of products of all 3-tuples is F(B, 3) = 2*3*4+2*3*5+3*4*5+2*4*5He was then given a number Q, number of queries of two types:   Type 1: Given q, i, and d calculate F(B(q, A), K) where we make change to initial array as A[i] = d.  Type 2: Given q, L, R, and d calculate F(B(q, A), K) where we make change to initial array as A[i] = A[i] + d for all i in range [L, R] inclusive. All changes are temporarily made to initial array, and don't propagate to following queries. Help the adventurer calculate the answer to a quest, and finally get that loot!InputIn the first two lines, numbers N (1 \leq N \leq 2*10^4) and K (1 \leq K \leq N), the length of initial array A, and tuple size, followed by a_1,a_2,a_3,…,a_N (0 \leq a_i \leq 10^9) , elements of array A, in the next line. Then follows number Q (Q \leq 10), number of queries. In the next Q lines come queries of the form:   1 q i d, for type 1,  2 q L R d, for type 2, as explained above (0 \leq q, d \leq 10^9, 1 \leq i,L,R \leq N)OutputPrint Q lines, the answers to queries, modulo 998244353.ExampleInput
5
2
1 2 3 4 5
3
1 6 1 1
1 6 5 2
2 6 2 3 1
Output
85
127
63
NoteIn the first query array A = [1, 2, 3, 4, 5], B = [5, 4, 3, 2, 1], sum of products of 2-tuples = 85.In second query array A = [1, 2, 3, 4, 2], B = [5, 4, 3, 2, 4], sum of products of 2-tuples = 127In third query array A = [1, 3, 4, 4, 5], B = [5, 3, 2, 2, 1], sum of products of 2-tuples = 63
5
2
1 2 3 4 5
3
1 6 1 1
1 6 5 2
2 6 2 3 1

85 127 63 
['divide and conquer', 'fft', '*2500']