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
import math
MAX_C = 10**9 + 7

mat = [[0]*13 for _ in range(100000)]

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

if s[0] == -1:
    for i in range(10):
        mat[0][i] = 1
else:
    mat[0][s[0]] = 1

for col_i in range(1, len(s)):
    for p_row_i in range(13):
        if mat[col_i-1][p_row_i] != 0:
            if mat[col_i-1][p_row_i] != 0:
                p_v = p_row_i
            else:
                p_v = 0

            if s[col_i] == -1:
                for n_v in range(10):
                    v = 10 * p_v + n_v
                    mat[col_i][v % 13] += mat[col_i-1][p_row_i]

            else:
                v = 10 * p_v + s[col_i]
                mat[col_i][v % 13] += mat[col_i-1][p_row_i]

    for i in range(13):
        mat[col_i][i] %= MAX_C

print(mat[len(s)-1][5])