Product Tuples
By Microsoft 
Serbia
By Microsoft Serbia
While 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 = a1 , a2 , ..., aN of length N , and a number K.
Define array B as B(q, A) = q − a1 , q − a2 , ..., q − aN . 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 ∗ 5
He 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!
In the first two lines, numbers N (1 ≤ N ≤ 2 ∗ 104 ) and K (1 ≤ K ≤ N ), the length of initial array A, and tuple size, followed by a1 , a2 , a3 , . . . , aN (0 ≤ ai ≤ 109 ) , elements of array A, in the next line. Then follows number Q (Q ≤ 10), number of queries. In the next Q lines come queries of the form:
• 1 q, i and d, for type 1,
• 2 q, L and R d, for type 2,
as explained above (0 ≤ q, d ≤ 109 , 1 ≤ i, L, R ≤ N )
Print Q lines, the answers to queries, modulo 998244353.
| Input Sample | Output Sample |
|
5 2 1 2 3 4 5 3 1 6 1 1 1 6 5 2 2 6 2 3 1 |
85 |