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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

# import time

N,P = list(map(int,input().split()))
S = input()

if P == 2:
    c = 0
    for i in range(N):
        u = int(S[i])
        if u % 2 == 0:
            c += i+1
    print(c)
        
elif P == 5:
    c = 0
    for i in range(N):
        u = int(S[i])
        if u % 5 == 0:
            c += i+1
    print(c)

else:
    U = [0]
    a = 0
    t = 1
    
    for i in range(N):
        t %= P
        a += int(S[-i-1])*t
        a %= P
        t *= 10
        U.append(a)
    # print(U)
    
    # t3 = time.time()
    
    c = 0
    
    """
    for i in range(P):
        m = U.count(i)
        c += m*(m-1)//2
    print(c)
    """
    U.sort()
    # print(U)
    q = -1
    for i in range(N):
        if q != U[i]:
            q = U[i]
            m = U.count(q)
            c += m*(m-1)//2
    print(c)
    
    # t4 = time.time()
    # print(t4-t3)
    
    # 10032