Description

Input

Each test contains multiple test cases. The first line contains the number of test cases $t\ (1 \leq t \leq 10^4)$. The description of the test cases follows.

The first and only line of each test case contains three integers $n$, $m$, and $b_0$ ($1 \leq n \leq 2 \cdot 10^5$, $1 \leq m \leq 2 \cdot 10^5$, $0 \leq b_0 \leq 2\cdot 10^5$) — the length of the array $a_1, \ldots, a_n$, the maximum possible element in $a_1, \ldots, a_n$, and the initial element of the array $b_0, \ldots, b_n$.

It is guaranteed that the sum of $n$ over all test cases does not exceeds $2\cdot 10^5$.

Output

For each test case, output a single line containing an integer: the number of different arrays $a_1, \ldots, a_n$ satisfying the conditions, modulo $998\,244\,353$.

6
3 2 1
5 5 3
13 4 1
100 6 7
100 11 3
1000 424 132
 
 
 

6
3120
59982228
943484039
644081522
501350342

Note

In the first test case, for example, when $a = [1, 2, 1]$, we can set $b = [1, 0, 1, 0]$. When $a = [1, 1, 2]$, we can set $b = [1, 2, 3, 4]$. In total, there are $6$ valid choices of $a_1, \ldots, a_n$: in fact, it can be proved that only $a = [2, 1, 1]$ and $a = [2, 1, 2]$ make it impossible to construct a non-negative continuous $b_0, \ldots, b_n$, so the answer is $2^3 - 2 = 6$.