there are $N$ items,which has values from 0 to $N-1$,find a subset of the items(you can choose nothing),you need to make the sum of the subset $S\equiv 0(mod~M)$
what's more,we make the rule that $K$ values $(a_1,a_2..a_K)$cannot be chosen.
please output the number of ways module 998244353
输入解释
the first line contains a number $T$,means the number of the test cases.
next,for each test case,the first line contains three numbers,$N,M,K$.
next line contains $K$ distinct numbers,$a_1,a_2..a_K$,means the numbers cannot be chosen.
$T\le 200,N\le 10^9,m\le 2048,K\le 4000$,$M$ is the Power of 2.
Only for 4 test cases there are $m>200$.
输出解释
$T$ lines,for each test case,output the answer.
输入样例
1
6 8 1
2
输出样例
6
six ways:
$0+1+3+4=8$
$1+3+4=8$
$0+3+5=8$
$3+5=8$
$0$
choose nothing($S=0$)