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: Wrong Answer)

import sys


sys.setrecursionlimit(10 ** 6)
INF = float("inf")
MOD = 10 ** 9 + 7


def input():
    return sys.stdin.readline().strip()


def main():
    S = input()
    N = len(S)
    dp = [[0] * 13 for _ in range(N)]

    if S[-1] == "?":
        for i in range(10):
            dp[0][i] = 1
    else:
        dp[0][int(S[-1])] = 1

    tenfactor = 1
    for i in range(1, N):
        tenfactor *= 10
        tenfactor %= MOD

        if S[N - i - 1] != "?":
            for k in range(13):
                j = int(S[N - i - 1])
                idx = (k + j * tenfactor) % 13
                dp[i][idx] += dp[i - 1][k]
                dp[i][idx] %= MOD
        else:
            for j in range(10):
                for k in range(13):
                    idx = (k + j * tenfactor) % 13
                    dp[i][idx] += dp[i - 1][k]
                    dp[i][idx] %= MOD

    print(dp[-1][5])


if __name__ == "__main__":
    main()