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: Time Limit Exceeded)

import sys
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
mod = 10**9 + 7
inf = float('inf')
ans = int(0)

S = str(input())
N = len(S)
M = 13
c = [0]*(N)
for i in range(N):
#    c[i] = (10**i)%M
    c[i] = pow(10,i,M)
#print(c)
c.reverse()
#print(c)
"""
dp = [[0]*M for _ in range(N+1)]
i = int(0)
for j in range(M):
    dp[0][j] = 1
for s in S:
    if s == "?":
        for l in range(10):
            m = l * c[i] % M
            dp[i+1][(M - m) % M] += dp[i][j]
    else:
        m = int(s) * c[i] % M
        dp[i][(M - m) % M] +=dp[i][j]
    i +=1
"""
dp = [[0]*M for _ in range(N)]
if S[0] == "?":
    for l in range(10):
        m = l * c[0]%M
        dp[0][m] += 1
else:
    m = int(S[0]) * c[0]%M
    dp[0][m] = 1
S = S[1:]
i = int(1)
for s in S:
    if s == "?":
        for j in range(M):
            for l in range(10):
                m = l*c[i]%M
                dp[i][j] += dp[i-1][(M+j-m)%M]
    else:
        for j in range(M):
            m = int(s)*c[i]%M
            dp[i][j] = dp[i-1][(M+j-m)%M]
    i +=1

"""
dp = [[0]*M for _ in range(N)]
if S[0] == "?":
    for l in range(10):
        m = l * c[0]%M
        dp[0][m] += 1
else:
    m = int(S[0]) * c[0]%M
    dp[0][m] = 1

for i in range(1,N):
    if S[i] == "?":
        for j in range(M):
            for l in range(10):
                m = l*c[i]%M
                dp[i][j] += dp[i-1][(M+j-m)%M]
    else:
        for j in range(M):
            m = int(S[i])*c[i]%M
            dp[i][j] = dp[i-1][(M+j-m)%M]
"""
#print(dp)
print(dp[N-1][5]%mod)