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: Runtime Error)

import math
import copy
from copy import deepcopy
import sys
import fractions
import numpy as np
from functools import reduce
import statistics
import heapq

# input = sys.stdin.readline
# sys.setrecursionlimit(10**6)

# ===FUNCTION===

def getInputInt():
    inputNum = int(input())
    return inputNum


def getInputListInt():
    outputData = []
    inputData = input().split()
    outputData = [int(n) for n in inputData]

    return outputData


def getSomeInputInt(n):
    outputDataList = []
    for i in range(n):
        inputData = int(input())
        outputDataList.append(inputData)

    return outputDataList


def getSomeInputListInt(n):
    inputDataList = []
    outputDataList = []
    for i in range(n):
        inputData = input().split()
        inputDataList = [int(n) for n in inputData]
        outputDataList.append(inputDataList)

    return outputDataList


# ===CODE===

def getInputStr():
    inputStr = str(input())
    return inputStr

data = getInputStr()

a = str(data)
listStr = []
listStr = list(a)

n = len(listStr)
# listStr.reverse()

dp = [[0]*13 for _ in range(len(listStr)+1)]
dp[0][0] = 1

# MOD = 10 ** 9 + 7
MOD = 1000000000 + 7

for i in range(n):
    if listStr[i] == "?":
        c = -1
    else:
        c = int(listStr[i])

    for j in range(10):
        if c != -1 and c != j:
            continue
        for ki in range(13):
            dp[i+1][(ki *10 + j) % 13] += dp[i][ki]

    for j in range(13):
        dp[i+1][j] %= MOD
res = dp[n][5]
print(res)


# for i in range(len(listStr)):
#     # keta = pow(10, i) % 13
#
#     if listStr[i] == "?":
#         for k in range(10):
#             for j in range(13):
#                 dp[i+1][int(((k*keta)%13 + j) % 13)] += dp[i][j]
#                 # dp[i+1][int(((k*keta)%13 + j) % 13)] += dp[i][j]
#     else:
#         k = int(listStr[i])
#         for j in range(13):
#             dp[i + 1][int(((k * keta) % 13 + j) % 13)] += dp[i][j]
#
# ans = dp[len(listStr)][5] % INF
# print(ans)