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 Python (3.4.3) (judge verdict: Wrong Answer)

####

import numpy as np
from numpy import newaxis, float32, float64, int32, int64, int16, int8, uint8, uint32, complex64, complex128

#####

def getIntList(inp):
	return [int(_) for _ in inp]


from sys import stdin
import sys

def getInputs():
	inputs=[]
	for line in stdin:
		line=line.split()
		inputs.append(line)
	return inputs


def main(inputs):
	n,p=getIntList(inputs[0])
	s=inputs[1][0]
	
	ans=0
	if p%2==0 or p%5==0:
		for i0 in range(len(s)-1,-1,-1):
			sub=int(s[i0:i0+1])
			if sub%p==0:
				ans+=i0+1
	else:
		numP0=np.zeros(p, int32)
		numP0[0]=1
		r=0
		for i0 in range(len(s)-1,-1,-1):
			sub=s[i0:i0+1]
			sub=int(sub)
			sub=r*10+sub
			sub%=p
			ans+=numP0[sub]
			numP0[sub]+=1
			r=sub
# 			print(s[i0:], sub, numP0, ans)
	print(ans)
		

if __name__=="__main__":
	inputs=getInputs()
# 	inputs=simInputs()
	main(inputs)