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 PyPy3 (2.4.0) (judge verdict: Accepted)

#!/usr/bin/env python3

import sys

sys.setrecursionlimit(10**7)

# Override `input` function because `stdin.readline()` is 10x faster than built-in `input()`
input = sys.stdin.readline


def read_h(typ=int):
    return list(map(typ, input().split()))


def read_v(n, m=1, typ=int):
    return [read_h(typ) if m > 1 else typ(input()) for _ in range(n)]


def main():
    S, = read_h(typ=str)
    n = len(S)

    MOD = 10**9 + 7

    dp = [[0] * 13 for _ in range(10**5 + 2)]
    dp[0][0] = 1
    #  print('initial dp:', dp)

    for i, s in enumerate(S):
        c = -1 if s == '?' else ord(s) - ord('0')
        #  print('c:', c)

        for j in range(10):
            if c != -1 and c != j:
                continue

            for k in range(13):
                dp[i + 1][(k * 10 + j) % 13] += dp[i][k]

            #  print('updated dp:', dp[:])

        for j in range(13):
            dp[i + 1][j] %= MOD

        #  print('final dp:', dp[:])

    res = dp[n][5]
    print(res)


if __name__ == '__main__':
    main()