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

s=input()
n=len(s)
dp=[list(0 for i in range(13)) for j in range(n)]
MOD=10**9+7
if s[0]=="?":
    for k in range(0,10):
        dp[0][k]+=1
else:
    dp[0][int(s[0])]+=1
for i in range(0,n-1):
    for k in range(13):
        if s[i+1]=="?":
            for j in range(10):
                ct=(k*10+j)%13
                dp[i+1][ct]+=dp[i][k]
                dp[i+1][ct]%=MOD
        elif s[i+1]!="?":
            tmp=(int(s[i+1])+k*10)%13
            dp[i+1][tmp]+=dp[i][k]
            dp[i+1][tmp]%=MOD
print(dp[n-1][5])