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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
ll n,p;
string s;
ll d[200005],e[200005];
ll a;
ll ans;
int main(void){
	cin>>n>>p>>s;
	ll D=1;
	for(int i=n-1;i>=0;i--){
		a=s[i]-48;
		d[i]=D*a%p;
		D=D*10%p;
	}
	if(p==2||p==5){
		for(int i=0;i<n;i++){
			if((s[i]-48)%p==0){
				ans+=i+1;
			}
		}
		cout<<ans<<endl;
		return 0;
	}
	for(int i=0;i<n;i++){
		e[i+1]=(e[i]+d[i])%p;
	}
	sort(e,e+n+1);
	ll co=1;
	for(int i=0;i<n;i++){
		if(e[i]==e[i+1]){
			co++;
		}else{
			ans+=co*(co-1)/2;
			co=1;
		}
	}
	ans+=co*(co-1)/2;
	cout<<ans<<endl;
	
}