Problem:
Score : 400 points

Problem Statement

Given is a string S. Each character in S is either a digit (0, ..., 9) or ?.

Among the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.

Since the answer can be enormous, print the count modulo 10^9+7.

Constraints

S is a string consisting of digits (0, ..., 9) and ?.

1 \leq |S| \leq 10^5

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

??2??5

Sample Output 1

768

For example, 482305, 002865, and 972665 satisfy the condition.

Sample Input 2

?44

Sample Output 2

1

Only 044 satisfies the condition.

Sample Input 3

7?4

Sample Output 3

0

We may not be able to produce an integer satisfying the condition.

Sample Input 4

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

Sample Output 4

153716888

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

S = input()
N = len(S)
DP =[0]*13
DP[0] = 1
A = 0
MOD = 10**9+7

B = [[0]*13 for i in range(13)]
for i in range(13):
    for j in range(13):
        B[i][j] = (i*j)%13
T = [1,10,9,12,3,4]
A = 0
for i in range(N):
    A*=10
    if S[i] == "?":
        hoge = [0]*13
        for j in range(13):
            for k in range(10):
                hoge[(j+k*T[(N-i-1)%6])%13] = (hoge[(j+k*T[(N-i-1)%6])%13] + DP[j])%MOD
        DP = hoge.copy()
    else:
        A = (A+int(S[i]))%13
print(DP[(A+5)%13])