Score : $500$ points
Given are $M$ digits $C_i$.
Find the sum, modulo $998244353$, of all integers between $1$ and $N$ (inclusive) that contain all of $C_1, \ldots, C_M$ when written in base $10$ without unnecessary leading zeros.
Input is given from Standard Input in the following format:
$N$ $M$ $C_1$ $\ldots$ $C_M$
Print the answer.
104 2 0 1
520
Between $1$ and $104$, there are six integers that contain both 0
and 1
when written in base $10$: $10,100,101,102,103,104$.
The sum of them is $520$.
999 4 1 2 3 4
0
Between $1$ and $999$, no integer contains all of 1
, 2
, 3
, 4
.
1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 5 0 2 4 6 8
397365274
Be sure to find the sum modulo $998244353$.