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 (7.3.0) (judge verdict: Accepted)

import math
from math import gcd,pi,sqrt
INF = float("inf")
MOD = 10**9 + 7

import sys
sys.setrecursionlimit(10**6)
import itertools
from collections import Counter,deque
def i_input(): return int(input())
def i_map(): return map(int, input().split())
def i_list(): return list(i_map())
def i_row(N): return [i_input() for _ in range(N)]
def i_row_list(N): return [i_list() for _ in range(N)]
def s_input(): return input()
def s_map(): return input().split()
def s_list(): return list(s_map())
def s_row(N): return [s_input for _ in range(N)]
def s_row_str(N): return [s_list() for _ in range(N)]
def s_row_list(N): return [list(s_input()) for _ in range(N)]

def main():
    s = input()
    n = len(s)
    dp = [[0]*13 for i in range(n+1)]
    dp[0][0] = 1

    for i,s in enumerate(s[::-1],start = 1):
        p10 = pow(10,i-1,13)
        if s!= "?":
            for k in range(13):
                dp[i][(int(s)*p10 + k)%13] += dp[i-1][k]
                dp[i][(int(s)*p10 + k)%13] %= MOD
        else:
            for j in range(10):
                for k in range(13):
                    dp[i][(j*p10 + k)%13] += dp[i-1][k]
                    dp[i][(j*p10 + k)%13] %= MOD
    print(dp[n][5] % MOD)


if __name__=="__main__":
    main()