Lowbit

Lucida has a sequence of $n$ integers $a_1, a_2, \dots, a_n$. He asks you to perform two types of operations for him, which are described as follows:

• $\texttt{1 L R}$, add $lowbit(a_i)$ to each $a_i$ in the interval $[L, R]$.


• $\texttt{2 L R}$, query the sum of the numbers in the interval $[L, R]$.

$lowbit(x)$ is defined as the largest power of 2 that divides $x$.
For example, lowbit(4)=4, lowbit(5)=1. Specially, lowbit(0)=0.

Lucida wants you to give the answer modulo $998244353$ for each of his queries.

This problem contains multiple test cases.

The first line contains a single integer $T$ ($1\leq T \leq 20$) indicating the number of test cases.

For each case, the first line contains an integer $n$ ($1 \leq n \leq 10^5$), the length of the sequence.

The next line contains $n$ integers $a_i$ ($1 \leq a_i < 998244353$) separated by spaces, representing the sequence.

The next line contains an integer $m$ ($1 \leq m \leq 10^5$), the number of operations.

The next $m$ lines, each line contains 3 integers $op, L, R$ ($1 \leq op \leq 2$, $1 \leq L \leq R \leq n$), represents one operation. The specific meaning is described above.

For each query, output a line contains the answer modulo $998244353$.

1
5
1 2 3 4 5
5
2 2 4
1 1 3
2 2 4
1 1 5
2 4 5

9
12
14

“红旗杯”第十五届东北地区大学生程序设计竞赛