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)

import sys
input = sys.stdin.readline

DIV = 10**9+7
s = input()
n = len(s)-1
ary = [ (int(s[i]) if s[i] != '?' else -1) for i in range(n) ]
dp = [ [0 for _ in range(13)] for _ in range(n+1) ]
dp[0][0] = 1
for i in range(n):
    for j in range(10):
        if ary[i] != -1 and ary[i] != j:
            continue
        for k in range(13):
            dp[i+1][(k*10+j)%13] += dp[i][k]

    for j in range(13):
        dp[i+1][j] %= DIV
print(dp[n][5])