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 \(A = {a_1,a_2,...,a_N }\) 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*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!
Output
Print \(Q\) lines, the answers to queries, modulo \(998244353\).
Note
In 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 = 127
In third query array A = [1, 3, 4, 4, 5], B = [5, 3, 2, 2, 1], sum of products of 2-tuples = 63
Примеры
| № | Входные данные | Выходные данные |
|
1
|
5
2
1 2 3 4 5
3
1 6 1 1
1 6 5 2
2 6 2 3 1
|
85
127
63
|