Problem: 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.

Submission attempts (in order):
def main():
    n = 13
    mod = 1000000007
    r = 5
    in_str = input()

    amari_list = amari(n)
    l = len(amari_list)

    ans_list = initial(in_str[-1:], n)

    for i, s in enumerate(reversed(in_str)):
        if i == 0:
            continue
        if s == "?":
            shift_list = [shift(j * amari_list[i % l] % n, ans_list)
                          for j in range(10)]

            ans_list = add(shift_list, mod)

        else:
            t = int(s) * amari_list[i % l] % n
            ans_list = shift(t, ans_list)

    print(ans_list[r] % mod)


def shift(r, num_list):
    l = len(num_list)
    return np.array([num_list[(i + l - r) % l] for i in range(l)], dtype='int64')


def add(num_list, mod):
    return np.sum(num_list, axis=0) % mod


def initial(s, n):
    if s == "?":
        return [1 if i < 10 else 0 for i in range(n)]
    else:
        return [1 if i == int(s) else 0 for i in range(n)]


def amari(n):
    ret = []
    for i in range(n+1):
        r = (10**i) % n
        if r in ret:
            return ret
        else:
            ret.append(r)


if __name__ == '__main__':
    main()


def main():
    n = 13
    mod = 1000000007
    r = 5
    in_str = input()

    amari_list = amari(n)
    l = len(amari_list)

    ans_list = initial(in_str[-1:], n)

    for i, s in enumerate(reversed(in_str)):
        if i == 0:
            continue
        if s == "?":
            shift_list = np.array([shift(j * amari_list[i % l] % n, ans_list)
                                   for j in range(10)], dtype='int64')

            ans_list = np.mod(np.sum(shift_list, axis=0), mod)

        else:
            t = int(s) * amari_list[i % l] % n
            ans_list = shift(t, ans_list)

    print(ans_list[r] % mod)


def shift(r, num_list):
    l = len(num_list)
    return np.array([num_list[(i + l - r) % l] for i in range(l)], dtype='int64')


def initial(s, n):
    if s == "?":
        return np.array([1 if i < 10 else 0 for i in range(n)], dtype='int64')
    else:
        return np.array([1 if i == int(s) else 0 for i in range(n)], dtype='int64')


def amari(n):
    ret = []
    for i in range(n+1):
        r = (10**i) % n
        if r in ret:
            return ret
        else:
            ret.append(r)


if __name__ == '__main__':
    main()

def main():
    n = 13
    mod = 1000000007
    r = 5
    in_str = input()

    amari_list = amari(n)
    l = len(amari_list)

    ans_list = initial(in_str[-1:], n)

    for i, s in enumerate(reversed(in_str)):
        if i == 0:
            continue
        if s == "?":
            tmp_list, ans_list = ans_list, [0]*n
            for j in range(10):
                t = j * amari_list[i % l] % n
                ans_list = [tmp_list[(i + l - t) % n] + ans_list[i]
                            for i in range(n)]
        else:
            t = int(s) * amari_list[i % l] % n
            ans_list = [ans_list[(i + l - t) % n] for i in range(n)]

        ans_list = list(map(lambda x: x % mod, ans_list))

    print(ans_list[r] % mod)


def initial(s, n):
    if s == "?":
        return [1 if i < 10 else 0 for i in range(n)]
    else:
        return [1 if i == int(s) else 0 for i in range(n)]


def amari(n):
    ret = []
    for i in range(n+1):
        r = (10**i) % n
        if r in ret:
            return ret
        else:
            ret.append(r)


if __name__ == '__main__':
    main()


import numpy as np


def main():
    n = 13
    mod = 1000000007
    r = 5
    in_str = input()

    amari_l = amari_list(n)
    amari_m = amari_matrix(n, amari_l)

    ans_list = initial(in_str[-1:], n)

    for i, s in enumerate(reversed(in_str)):
        if i == 0:
            continue
        if s == "?":
            ans_list = np.dot(ans_list, amari_m[i % len(amari_m)]) % mod
        else:
            t = int(s) * amari_l[i % len(amari_l)] % n
            ans_list = np.roll(ans_list, t)

    print(int(ans_list[r] % mod))


def initial(s, n):
    if s == "?":
        return np.array([1 if i < 10 else 0 for i in range(n)], dtype='int64')
    else:
        return np.array([1 if i == int(s) else 0 for i in range(n)], dtype='int64')


def shift(n, r):
    return np.array([[1 if (i - j + r) % n == 0 else 0 for j in range(n)] for i in range(n)])


def amari_list(n):
    ret = []
    for i in range(n + 1):
        r = 10**i % n
        if r in ret:
            return ret
        else:
            ret.append(r)


def amari_matrix(n, amari_list):
    ret = np.zeros((len(amari_list), n, n))
    for i, j in enumerate(amari_list):
        tmp = np.zeros((n, n))
        for k in range(10):
            tmp += shift(n, j * k % n)
        ret[i] = tmp
    return ret


if __name__ == '__main__':
    main()


Verdicts: Runtime Error

Runtime Error

Wrong Answer

Accepted