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: Wrong Answer)

package main

import (
        "fmt"
        "strconv"
        "strings"
)

func calc(p int, s string, c map[string]bool) bool {
        t := strings.TrimLeft(s, "0")
        r, ok := c[t]
        if ok {
                return r
        }
        if len(t) < 10 {
                v, _ := strconv.Atoi(t)
                c[t] = int(v)%p == 0
                return c[t]
        }
        v, _ := strconv.Atoi(t[0:10])
        s = s[10:]
        u := v % p
        for len(s) > 0 {
                v, _ := strconv.Atoi(t[0:1])
                u = (u*10 + v) % p
                s = s[1:]
        }
        c[t] = u == 0
        return c[t]

}
func main() {
        var N, P int
        fmt.Scanf("%d %d", &N, &P)
        lp := len(fmt.Sprintf("%d", P))
        c := map[string]bool{}
        var S string
        fmt.Scanf("%s", &S)
        ret := 0
        for i := 0; i <= N-lp; i++ {
                for j := i + lp - 1; j <= N; j++ {
                        if calc(P, S[i:j], c) {
                                ret += 1
                        }
                }
        }
        fmt.Println(ret)
}