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: Wrong Answer)

fun main(args: Array<String>) {
    val (n, p) = readInts()
    assert(n % 2 == 1 || n % 2 == 0)
    val s = readLn()

    val modP = mutableListOf<Int>()
    var mul = 1
    for (i in s.length - 1 downTo 0) {
        val num = s[i] - '0'
        modP.add(((if (modP.isNotEmpty()) modP.last() else 0) + mul * num) % p)
        mul = (mul * 10) % p
    }

    val occurs = mutableMapOf<Int, Int>()
    occurs[0] = 1
    modP.forEach {
        occurs[it] = occurs[it]?.plus(1) ?: 1
    }

    var ans = 0L
    occurs.forEach { entry ->
        val occ = entry.value
        ans += (occ.toLong() * (occ - 1)) / 2
    }
    println(ans)
}

// Input Reader
private fun readLn() = readLine()!!

private fun readStrings() = readLn().trim().split(" ")
private fun readInts() = readStrings().map { it.toInt() }