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: Runtime Error)

s = input()

DIV = 13
MOD = 10**9+7
dp = [[0 for x in range(DIV)] for y in range(len(s))]

tmp = s[-1]
if tmp == '?':
    for j in range(10):
        dp[0][j%DIV] += 1
else:
    dp[0][int(tmp)%DIV] += 1

for i in range(1, len(s)):
    tmp = s[len(s)-i-1]
    if tmp == '?':
        for j in range(10):
            for k in range(DIV):
                dp[i][(j*10**i+k)%DIV] += dp[i-1][k]
    else:
        for k in range(DIV):
            dp[i][(int(tmp)*10**i+k)%DIV] += dp[i-1][k]

    for k in range(DIV):
        dp[-1][i] %= MOD

print(dp[-1][5])