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: Runtime Error)

S = input()

# 桁数
N = len(S)
MOD = 10**9 + 7

# dp[i][j] := Sの上からi桁目までを考えた時、それを13で割った余りがjになる方法の数
dp = [[0 for _ in range(13)]for _ in range(N + 1)]

# １桁目について
if S[0] == "?":
    # ?に0, 1, ..., 9を入れることができる
    for i in range(10):
        dp[1][i] = 1
else:
    dp[1][S[0]] = 1

# 1, 2, ..., N-1桁から、
# 2, 3, ..., N桁についての遷移を考える
for i in range(1, N):
    for j in range(13):
        if S[i] == "?":
            for k in range(10):
                dp[i + 1][(j * 10 + k) % 13] += dp[i][j]
                dp[i + 1][(j * 10 + k) % 13] %= MOD
        else:
            dp[i + 1][(j * 10 + int(S[i])) % 13] += dp[i][j]
            dp[i + 1][(j * 10 + int(S[i])) % 13] %= MOD

print(dp[N][5] % MOD)