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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n, p int
	var s string
	fmt.Scan(&n, &p, &s)

	if p == 2 || p == 5 {
		res := 0
		for i := 0; i < n; i++ {
			if int(s[i]-'0')%p == 0 {
				res += i + 1
			}
		}
		fmt.Println(res)
		return
	}

	r := make([]int, n+1)
	d := 1
	for i := n - 1; i >= 0; i-- {
		x := int(s[i]-'0') * d % p
		r[i] = (x + r[i+1]) % p
		d *= 10
		d %= p
	}

	res := 0
	cnt := make(map[int]int)
	for i := n; i >= 0; i-- {
		res += cnt[r[i]]
		cnt[r[i]]++
	}

	fmt.Println(res)
}