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: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"math/big"
	"os"
	"strconv"
)

// N: [1, 2e5]
// len(S) = N
// P: [2, 10000], prime
func main() {
	sc := newInputScanner(true, 256)
	N, P, S := sc.nextInt(), sc.nextInt(), sc.nextStr()
	// N := 20000
	// P := 127
	// S := ""
	// for i := 0; i < N; i++ {
	// 	S += string(strconv.Itoa(rand.Intn(10)))
	// }
	// fmt.Println(S)
	answer := checkSubNumbers(N, P, S)
	fmt.Println(answer)
}

func checkSubNumbers(N int, P int, S string) int {
	switch P {
	case 2, 5:
		return checkTwoOrFive(N, P, S)
	default:
		return checkNotTwoNorFive(N, P, S)
	}
}

func checkTwoOrFive(N int, P int, S string) int {
	answer := 0
	var n int
	for i := N - 1; i >= 0; i-- {
		n, _ = strconv.Atoi(S[i : i+1])
		if n%P == 0 {
			answer += i + 1
		}
	}
	return answer
}

func checkNotTwoNorFive(N int, P int, S string) int {
	bigP := big.NewInt(int64(P))
	ten := big.NewInt(10)
	multiplier := big.NewInt(1)
	answer := 0
	remainderLookup := make([]int, P)
	currentBigInt := big.NewInt(0)
	prevRemaider := -1
	var digit, remainder, count int
	var n *big.Int
	for i := N - 1; i >= 0; i-- {
		digit, _ = strconv.Atoi(S[i : i+1])
		if digit == 0 {
			if prevRemaider == -1 {
				remainder = 0
			} else {
				remainder = prevRemaider
			}
		} else {
			n = big.NewInt(int64(digit))
			n = n.Mul(n, multiplier)
			n = n.Add(currentBigInt, n)
			currentBigInt.Set(n)
			remainder = int(n.Mod(n, bigP).Int64())
		}
		if remainder == 0 {
			answer++
		}
		count = remainderLookup[remainder]
		answer += count
		count++
		remainderLookup[remainder] = count
		prevRemaider = remainder
		multiplier = multiplier.Mul(multiplier, ten)
	}
	return answer
}

type inputScanner struct {
	*bufio.Scanner
}

func newInputScanner(enabledScanWords bool, sizeInKB int) *inputScanner {
	scanner := bufio.NewScanner(os.Stdin)
	if enabledScanWords {
		scanner.Split(bufio.ScanWords)
	}
	capacity := sizeInKB * 1024
	buf := make([]byte, capacity)
	scanner.Buffer(buf, capacity)
	return &inputScanner{
		Scanner: scanner,
	}
}

func (inputSc *inputScanner) nextInt() int {
	i, e := strconv.Atoi(inputSc.nextStr())
	if e != nil {
		panic(e)
	}
	return i
}

func (inputSc *inputScanner) nextUInt64() uint64 {
	i, e := strconv.ParseUint(inputSc.nextStr(), 10, 64)
	if e != nil {
		panic(e)
	}
	return i
}

func (inputSc *inputScanner) nextStr() string {
	inputSc.Scan()
	return inputSc.Text()
}