Sum of the numbers with a fixed digit sum

Let $F(B,L,D)$ be the sum of all the L-digit numbers in base B, the digit sum of which is D.

For example, $F(3,3,3)=79$. In base 3, there are five 3-digit numbers the digit sum of which is 3. The sum of these five numbers is 79. $(102{)}_3+(111{)}_3+(120{)}_3+(201{)}_3+(210{)}_3=(2221{)}_3=(79{)}_{10}$

Now we define a new function $S(B,L,N)$ = ${\displaystyle \sum _{p\le N\text{, p is prime}}F(B,L,p)}$

For example, $S(5,5,11)=964140$ and $S(56,20,101)\equiv 913761394(\mathrm{mod}1000004321)$

Find $S(556678,999,12345701)mod1000004321$

Note:Leading zeroes are not allowed for a L-digit number in base B.