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 Kotlin (1.0.0) (judge verdict: Runtime Error)

fun main() {
    val (n, p) = readLine()!!.split(' ').map { it.toInt() }
    val s = readLine()!!

    val ans = if (10 % p == 0) {
        solve1(s, p)
    } else {
        solve2(s, p)
    }

    println(ans)
}

fun solve1(s: String, p: Int): Long {
    return s.indices
            .map { if ((s[it] - '0') % p == 0) it + 1L else 0L }
            .sum()
}

fun solve2(s: String, p: Int): Long {
    var r = 0L
    val s = s.reversed()

    var b = 1
    val a = IntArray(s.length)
    for (i in s.indices) {
        a[i] = (s[i] - '0') * b % p
        b = b * 10 % p
    }

    val cs = IntArray(s.length + 1)
    for (i in s.indices) {
        cs[i + 1] = (cs[i] + a[i]) % p
    }

    val cnt = IntArray(p)
    for (i in cs.indices) {
        r += cnt[cs[i]]++
    }

    return r
}