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
MAX_C = 10**9 + 7


s = input()
s = s[:len(s)-1]
n = len(s)
s = [-1 if s[i] == '?' else int(s[i]) for i in range(n)]

#mat = [[0]*13 for _ in range(n)]
p = [0]*13
np = [0]*13

list10 = list(range(10))
list13 = list(range(13))
mods = [i % 13 for i in range(130)]

if s[0] == -1:
    for i in list10:
        #mat[0][i] = 1
        p[i] = 1
else:
    #mat[0][s[0]] = 1
    p[s[0]] = 1

for col_i in range(1, n):
    n_w = s[col_i]
    if n_w == -1:
        for n_v in list10:
            for p_row_i in list13:
                v = 10*p_row_i + n_v
                #mat[col_i][mods[v]] += mat[col_i-1][p_row_i]
                np[mods[v]] += p[p_row_i]

    else:
        for p_row_i in list13:
            v = 10*p_row_i + s[col_i]
            #mat[col_i][mods[v]] += mat[col_i-1][p_row_i]
            np[mods[v]] += p[p_row_i]

    for i in list13:
        p[i] = np[i] % MAX_C
        np[i] = 0
        #mat[col_i][i] %= MAX_C

#print(mat[n-1][5])
print(p[5])