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



Sample input:
??2??5


Sample output:
768

Submission status: Accepted

Solution code:
S = input()
n = len(S)
mod = 10**9 + 7
pow10 = [1]
for i in range(1,n):
    x = pow10[-1]
    y = 10*x%13
    pow10.append(y)
dp = [[0 for i in range(13)]for j in range(n+1)]
dp[0][0] = 1
for i in range(n):
    d = S[-i-1]
    if d == '?':
        for j in range(10):
            s = (pow10[i]*j)%13
            for t in range(13):
                r = (s+t)%13
                dp[i+1][r] = (dp[i+1][r] + dp[i][t])%mod
    else:
        j = int(d)
        s = (pow10[i]*j)%13
        for t in range(13):
            r = (s+t)%13
            dp[i+1][r] = (dp[i+1][r] + dp[i][t])%mod
print(dp[n][5])

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    S = r()
    N = len(S)
    rem = 1 # remainder when devided by 13
    dp = [[0]*(N+1) for _ in range(13)]
    dp[0][0] = 1
    for i, s in enumerate(reversed(S)):
        if s == '?':
            for j in range(10):
                d = (rem*j)%13
                for k in range(13):
                    dp[(k+d)%13][i+1] = (dp[(k+d)%13][i+1] + dp[k][i]) % (10**9+7)
        else:
            ss = int(s)
            d = (rem*ss)%13
            for k in range(13):
                dp[(k+d)%13][i+1] = dp[k][i]
        # update 
        rem = rem*10%13
    print(dp[5][N])
        
    
    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
MOD = 10**9+7

S = input().rstrip("\n")

# dp[i][j]: i文字目でjになる個数 (S[-i])
# 1-indexed
dp = [[0]*13 for _ in range(len(S)+1)]

# 初期条件(1桁目)
if S[-1] == "?":
    dp[1][:10] = [1]*10
else:
    dp[1][int(S[-1])] += 1

# mul = 10**(i-1)
mul = 10
# i: i桁目
for i in range(2,len(S)+1):
    if S[-i] == "?":
        # j: S[-i]がとる値 (?のとき0~9)
        for j in range(10):
            jmod = j*mul % 13
            # (i-1)桁目で余りがkとなる個数x
            for k,x in enumerate(dp[i-1]):
                dp[i][(k+jmod)%13] = (dp[i][(k+jmod)%13] + x) % MOD
    else:
        jmod = int(S[-i])*mul % 13
        for k,x in enumerate(dp[i-1]):
            dp[i][(k+jmod)%13] = (dp[i][(k+jmod)%13] + x) % MOD
    mul = (mul * 10) % 13

print(dp[-1][5])

Submission status: Accepted

Solution code:
import numpy as np

S = input()
mod = int(10**9 + 7)
dp = np.zeros(13, dtype=int)
dp[0] = 1

M = np.zeros((13, 13), dtype=int)
for i in range(13):
    for d in range(10):
        M[i][(i * 10 + d) % 13] += 1

for s in S:
    ndp = np.zeros(13, dtype=int)
    if s == '?':
        ndp = np.dot(dp, M)
    else:
        d = int(s)
        for j in range(13):
            ndp[(j * 10 + d) % 13] += dp[j]
    dp = ndp % mod

print(dp[5])

Submission status: Accepted

Solution code:
import numpy as np

s = input()
p = np.array([0]*13)
p[0] = 1

amari = [[0]*13 for _ in range(13)]
for j in range(10):
  for i in range(13):
    amari[i][(i*10+j)%13] += 1
M = np.array(amari)

for si in range(len(s)):
  a = np.array([0]*13)
  if s[si] == '?':
    a = np.dot(p,M)
  else:
    c = int(s[si])
    for i in range(13):
      a[(i*10+c)%13] += p[i]
  p = np.mod(a,1000000007)
print(p[5])

Submission status: Accepted

Solution code:
import numpy as np
 
s = input()
p = np.array([0]*13)
p[0] = 1
 
amari = [[0]*13 for _ in range(13)]
for j in range(10):
  for i in range(13):
    amari[i][(i*10+j)%13] += 1
M = np.array(amari)
 
for si in range(len(s)):
  a = np.array([0]*13)
  if s[si] == '?':
    a = np.dot(p,M)
  else:
    c = int(s[si])
    for i in range(13):
      a[(i*10+c)%13] += p[i]
  p = np.mod(a,1000000007)
print(p[5])

Submission status: Accepted

Solution code:
import sys

if sys.platform =='ios':
	sys.stdin=open('Untitled.txt')
input = sys.stdin.readline
def INT(): return int(input())
def MAP(): return [int(s) for s in input().split()]

S = input().rstrip()

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

#print(dp)

for i in range(len(S)):
	for j in range(13):
		if S[i]=='?':
			for d in range(10):
				nj = (j*10+d)%13
				dp[i+1][nj] += dp[i][j]
		else:
			nj = (j*10+int(S[i]))%13
			dp[i+1][nj] += dp[i][j]
	for j in range(13):
		dp[i+1][j] %= (10**9+7)

#print(dp)
print(dp[len(S)][5])

Submission status: Accepted

Solution code:
s=input()
d=[0]*13
d[0]=1
for i in s:
    dnew=[0]*13
    if i=="?":
        for j in range(10):
            for k in range(13):
                dnew[(10*k+j)%13]+=d[k]
            for k in range(13):
                dnew[k]%=(10**9+7)
    else:
        for k in range(13):
            dnew[(10*k+int(i))%13]+=d[k]
        for k in range(13):
            dnew[k]%=(10**9+7)
    d=dnew

print(d[5])

Submission status: Accepted

Solution code:
s = input()

N = 13
dp = [0] * N
dp[0] = 1

mod = 10 ** 9 + 7
mul = 1
t = s[::-1]

for i in range(len(s)):
    nextDP = [0] * N
    c = t[i]
    if c == "?":
        for k in range(10):
            for j in range(N):
                nextDP[(k * mul + j) % N] += dp[j]
                nextDP[(k * mul + j) % N] %= mod
    else:
        k = int(t[i])
        for j in range(N):
            nextDP[(k * mul + j) % N] += dp[j]
            nextDP[(k * mul + j) % N] %= mod

    mul *= 10
    mul %= N
    dp = nextDP

print(dp[5])

Submission status: Accepted

Solution code:
#d
def main():
    s=input()
    n=len(s)
    mod=10**9+7
    
    if s[-1]=="?":
        dp=[1,1,1,1,1,1,1,1,1,1,0,0,0]
    else:
        dp=[0]*13
        dp[int(s[-1])]=1
    
    for i in range(1,n):
        imod=10**(i %12)
        ss0=s[n-i-1]
        if ss0!="?":
            dpnew = [ dp[(j-int(ss0)*imod)%13] %mod for j in range(13)]
        else:
            dpnew = [sum( dp[(j-k*imod)%13] for k in range(10)) %mod for j in range(13) ]
        dp=dpnew[:]
    print(dp[5])
    
if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
MOD = 10**9 + 7

def solve(s, p=13):
    a = [0] * p
    a[0] = 1
    for c in s:
        b = [0] * p
        for i in range(p):
            b[(i*10)%p] = a[i] % MOD
        b += b
        if c == "?":
            for i in range(p):
                a[i] = sum(b[i+4:i+p+1])
        else:
            for i in range(p):
                a[i] = b[i+p-int(c)]
    return a[5] % MOD

s = input()
print(solve(s))

Submission status: Accepted

Solution code:
#coding: utf-8
import math
import heapq
import bisect

MOD = 10**9+7

S = input()
ans = [1]+[0]*12
 
for c in S:
    dp=[0]*13
    for i in range(13):
        #dpはansを一桁ずらしたもの
        dp[(i*10)%13]=ans[i]%MOD
    #0~12と13~25と同じものを増設
    dp+=dp
 
    if c=='?':
        for i in range(13):
            #添字を13から26まで増やしたから、ここでこう楽な計算ができる。
            ans[i]=sum(dp[i+4:i+14])
    else:
        for i in range(13):
            ans[i]=dp[i+13-int(c)]

print(ans[5]%MOD)

Submission status: Accepted

Solution code:
#coding: utf-8
import math
import heapq
import bisect

MOD = 10**9+7

S = input()
ans = [0]*13
ans[0]=1
 
for c in S:
    dp=[0]*13
    for i in range(13):
        #dpはansを一桁ずらしたもの
        dp[(i*10)%13]=ans[i]%MOD
    #0~12と13~25と同じものを増設
    dp+=dp
 
    if c=='?':
        for i in range(13):
            #添字を13から26まで増やしたから、ここでこう楽な計算ができる。
            ans[i]=sum(dp[i+4:i+14])
    else:
        for i in range(13):
            ans[i]=dp[i+13-int(c)]

print(ans[5]%MOD)

Submission status: Accepted

Solution code:
s = input()
#文字の昇順に処理していきたいため、逆順にしておく
s = s[::-1]
mod = 7 + 10**9
keta = 1
dp = [[0 for i in range(13)] for j in range(len(s) + 1)]
dp[0][0] = 1
for i in range(len(s)):
    if s[i] != "?":
        k = (int(s[i]) * keta) % 13
        for j in range(13):
            dp[i + 1][(j + k) % 13] = dp[i][j]
    else:
        for j in range(13):
            for k in range(10):
                l = ( k * keta ) % 13
                dp[i + 1][(j + l) % 13] += dp[i][j] % mod
    keta = keta *10 % 13 
print(dp[-1][5] % mod)

Submission status: Accepted

Solution code:
MOD = 10**9+7
S = input()
LenS = len(S)
DP = [[0] * 13 for _ in range(LenS+1)]

c = S[0]
if c == '?':
    for i in range(10):
        DP[1][i] = 1
else:
    n = int(c)
    DP[1][n] = 1

for i in range(2,LenS+1):
    c = S[i-1]
    if c == '?':
        for n in range(10):
            for j in range(13):
                k = (10*j+n) % 13
                DP[i][k] += DP[i-1][j] 
                DP[i][k] %= MOD
    else:
        n = int(c)  
        for j in range(13):
            k = (10*j+n) % 13
            DP[i][k] = DP[i-1][j] 
            DP[i][k] %= MOD

print(DP[LenS][5])

Submission status: Accepted

Solution code:
MOD = 10 ** 9 + 7

S = input()
N = len(S)

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

mul = 1

for i, x in enumerate(S[::-1]):
  if x == "?":
    for k in range(10):
      for j in range(13):
        jj = (mul * k + j) % 13
        dp[i + 1][jj] += dp[i][j]
        dp[i + 1][jj] %= MOD
  else:
    k = int(x)
    for j in range(13):
      jj = (mul * k + j) % 13
      dp[i + 1][jj] += dp[i][j]
      dp[i + 1][jj] %= MOD

  mul = (mul * 10) % 13

print(dp[N][5])

Submission status: Accepted

Solution code:
s = input()[::-1]
cur = [0] * 13
MOD = 10**9+7
c = 1
cur[0] = 1
for i in range(len(s)):
  pre,cur = cur,[0]*13
  if s[i] == '?':
    for j in range(10):
      for k in range(13):
        cur[(k+j*c)%13] += pre[k]
  else:
    i = int(s[i])
    for j in range(13):
      cur[(j+i*c)%13] += pre[j]
  c = (c*10) % 13
  for i in range(13):
    cur[i] = cur[i] % MOD
print(cur[5])

Submission status: Accepted

Solution code:
S=input()
A=[1,0,0,0,0,0,0,0,0,0,0,0,0]
a=10**9+7
for i in range(len(S)):
  B=A[:]
  if S[i]=="?":
    A[0]=(B[0]+B[9]+B[5]+B[1]+B[10]+B[6]+B[2]+B[11]+B[7]+B[3])%a
    A[1]=(B[4]+B[0]+B[9]+B[5]+B[1]+B[10]+B[6]+B[2]+B[11]+B[7])%a
    A[2]=(B[8]+B[4]+B[0]+B[9]+B[5]+B[1]+B[10]+B[6]+B[2]+B[11])%a
    A[3]=(B[12]+B[8]+B[4]+B[0]+B[9]+B[5]+B[1]+B[10]+B[6]+B[2])%a
    A[4]=(B[3]+B[12]+B[8]+B[4]+B[0]+B[9]+B[5]+B[1]+B[10]+B[6])%a
    A[5]=(B[7]+B[3]+B[12]+B[8]+B[4]+B[0]+B[9]+B[5]+B[1]+B[10])%a
    A[6]=(B[11]+B[7]+B[3]+B[12]+B[8]+B[4]+B[0]+B[9]+B[5]+B[1])%a
    A[7]=(B[2]+B[11]+B[7]+B[3]+B[12]+B[8]+B[4]+B[0]+B[9]+B[5])%a
    A[8]=(B[6]+B[2]+B[11]+B[7]+B[3]+B[12]+B[8]+B[4]+B[0]+B[9])%a
    A[9]=(B[10]+B[6]+B[2]+B[11]+B[7]+B[3]+B[12]+B[8]+B[4]+B[0])%a
    A[10]=(B[1]+B[10]+B[6]+B[2]+B[11]+B[7]+B[3]+B[12]+B[8]+B[4])%a
    A[11]=(B[5]+B[1]+B[10]+B[6]+B[2]+B[11]+B[7]+B[3]+B[12]+B[8])%a
    A[12]=(B[9]+B[5]+B[1]+B[10]+B[6]+B[2]+B[11]+B[7]+B[3]+B[12])%a
  else:
    s=int(S[i])
    for i in range(13):
      A[i]=B[(i*4+9*s)%13]
print(A[5])

Submission status: Accepted

Solution code:
S=input()
a=[0]*13
a[0]= 1

for c in S:
  dp=[0]*13
  for i in range(13):
    dp[(i*10)%13]=a[i]%(10**9+7)
  dp+=dp

  if c=='?':
    for i in range(13):
      a[i]=sum(dp[i+4:i+14])
  else:
    for i in range(13):
      a[i]=dp[i+13-int(c)]

print(a[5]%(10**9+7))

Submission status: Accepted

Solution code:
import sys


def solve():
    readline = sys.stdin.buffer.readline
    mod = 10 ** 9 + 7
    s = str(readline().rstrip().decode('utf-8'))
    dp = [[0] * 13 for _ in range(len(s))]
    for i in range(len(s)):
        ts = s[-i-1]
        if i == 0:
            if ts == "?":
                for j in range(10):
                    dp[i][j] += 1
            else:
                dp[i][int(ts)] += 1
        else:
            mult = pow(10, i, 13)
            if ts == "?":
                for j in range(13):
                    for k in range(10):
                        dp[i][(k * mult + j) % 13] += dp[i-1][j]
            else:
                num = int(ts)
                for j in range(13):
                    dp[i][(num * mult + j) % 13] += dp[i-1][j]
            for j in range(13):
                dp[i][j] %= mod
    print(dp[-1][5] % mod)


if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
s = input()

dp = [[0 for i in range(13)] for j in range(len(s)+1)]

mod = 10**9+7
mul = 1
dp[0][0] = 1

for i in reversed(range(len(s))):
    keta = len(s) - i - 1
    if s[i] == '?':
        for k in range(10):
            for j in range(13):
                amari = (j+k*(mul)) % 13
                #print(amari,i)
                dp[keta+1][amari] += dp[keta][j]
                dp[keta+1][amari] %= mod
    else:
        num = int(s[i])
        for j in range(13):
            amari = (j+(num*(mul))) % 13
            #print(keta,amari)
            dp[keta+1][amari] += dp[keta][j]
            dp[keta+1][amari] %= mod
    mul = mul * 10 % 13
            
print(dp[len(s)][5])
#print(dp[len(s)][5])

Submission status: Accepted

Solution code:
s = input()
now = 1
dp0 = [[1] + [0] * 12]
dp = dp0 + [[0] * 13 for i in range(len(s))]
mod = 10 ** 9 + 7
for key,i in enumerate(s[::-1]):
  if i == "?":
    rem = 0
    rems = []
    for j in range(10):
      rems.append(rem)
      rem += now
      rem %= 13
    for index,j in enumerate(dp[key]):
      for rm in rems:
        dp[key+1][(index+rm)%13] += j % mod
  else:
    i = int(i)
    rm = now * i
    for index,j in enumerate(dp[key]):
      dp[key+1][(index+rm)%13] += j % mod
  now *= 10
  now %= 13
ans = dp[-1][5] % mod
print(ans)

Submission status: Accepted

Solution code:
S = list(reversed(input().strip()))

MOD = int(pow(10, 9) + 7)

powers = [1 for i in range(len(S))]
for i in range(1, len(S)):
    powers[i] = (10 * powers[i - 1]) % 13

dp = [[0 for i in range(13)] for j in range(len(S))]

for i, char in enumerate(S):
    def compute(num):
        if i == 0:
            # Base case
            dp[0][num] += 1
        else:
            for o in range(13):
                dp[i][(o + num * powers[i]) % 13] += dp[i - 1][o]
                dp[i][(o + num * powers[i]) % 13] %= MOD
                
    if char == "?":
        for j in range(10):
            compute(j)
    else:
        compute(int(char))

print(dp[-1][5])

Submission status: Accepted

Solution code:
from collections import Counter,defaultdict,deque
from heapq import heappop,heappush,heapify
import sys,bisect,math,itertools
sys.setrecursionlimit(10**8)
mod = 10**9+7
mod2 = 998244353
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpln(n): return list(int(sys.stdin.readline()) for i in range(n))

s = input()
n = len(s)
now = [0] * 13
now[0] = 1
for i in range(n)[::-1]:
    prev = now[::]
    now = [0] * 13
    c = n - i - 1#桁
    m = pow(10,c,13)
    if s[i] == '?':
        for k in range(10):
            l = (m*k) % 13
            for j in range(13):
                now[(j+l)%13] += prev[j]
                now[(j+l)%13] = now[(j+l)%13] % mod
    else:
        k = int(s[i])
        l = (m*k) % 13
        for j in range(13):
            now[(j+l)%13] = prev[j]
    # print(now)
print(now[5])