Problem:
Score : 500 points

Problem Statement

Takahashi has a string S of length N consisting of digits from 0 through 9.

He loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N \times (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.

Here substrings starting with a 0 also count, and substrings originated from different positions in S are distinguished, even if they are equal as strings or integers.

Compute this count to help Takahashi.

Constraints

1 \leq N \leq 2 \times 10^5

S consists of digits.

|S| = N

2 \leq P \leq 10000

P is a prime number.

Input

Input is given from Standard Input in the following format:

N P
S

Output

Print the number of non-empty (contiguous) substrings of S that are divisible by P when regarded as an integer written in base ten.

Sample Input 1

4 3
3543

Sample Output 1

6

Here S = 3543. There are ten non-empty (contiguous) substrings of S:

3: divisible by 3.

35: not divisible by 3.

354: divisible by 3.

3543: divisible by 3.

5: not divisible by 3.

54: divisible by 3.

543: divisible by 3.

4: not divisible by 3.

43: not divisible by 3.

3: divisible by 3.

Six of these are divisible by 3, so print 6.

Sample Input 2

4 2
2020

Sample Output 2

10

Here S = 2020. There are ten non-empty (contiguous) substrings of S, all of which are divisible by 2, so print 10.

Note that substrings beginning with a 0 also count.

Sample Input 3

20 11
33883322005544116655

Sample Output 3

68

Solution in Lua (5.3.2) (judge verdict: Wrong Answer)

n,p=io.read("*n","*n","*l")
s=io.read()

combination=0
if p==2 or p==5 then
    for i=1,n do
        x=tonumber(s:sub(i,i))
        if x%p==0 then
            combination=combination+1
        end
    end
    print(combination)
    return
end

t={}
for i=1,p do
    t[i]=0
end
t[1]=1
digit=1
smod=0
for i=1,n do
    x=tonumber(s:sub(i,i))
    smod=(smod+x*digit)%p
    combination=combination+t[smod+1]
    t[smod+1]=t[smod+1]+1
    digit=(digit*10)%p
end

print(combination)