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: Time Limit Exceeded)

S=input()
S=list(S)
dp=[]
for _ in range(len(S)):
    dp.append([0]*13)
if S[0]=='?':
    for i in range(10):
        dp[0][(i*10**(len(S)-1))%13]=1
else:
    dp[0][(int(S[0])*10**(len(S)-1))%13]=1
for j in range(0,len(S)-1):
    for k in range(13):
        if S[j+1]=='?':
            L=[]
            for l in range(10):
                l=(l*10**(len(S)-j-2)%13)
                L.append(dp[j][k-l])
            dp[j+1][k]+=sum(L)
        else:
            dp[j+1][k]=dp[j][k-(int(S[j+1]))*10**(len(S)-j-2)%13]
print((dp[len(S)-1][5])%(7+10**9))