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: Accepted)

fun main(args: Array<String>) {
    val (N, P) = readInputLine().split(" ").map { it.toInt() }
    val S = readInputLine().reversed().toCharArray()

    var ans = 0L

    if (P == 2 || P == 5) {
        for ((i, c) in S.withIndex()) {
            if ((c - '0') % P == 0) {
               ans += (N - i).toLong()
            }
        }
        println(ans)
        return
    }

    val modCnt = LongArray(P)
    modCnt[0]++

    var current = 0
    var digitFactor = 1
    for (c in S) {
        current = ((c - '0') * digitFactor + current) % P
        digitFactor = (digitFactor * 10) % P
        modCnt[current]++
    }

    repeat(P) {
        ans += modCnt[it] * (modCnt[it] - 1L) / 2L
    }

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}