Buggy python submission (verdict: Time Limit Exceeded):
MOD = 10 ** 9 + 7
S = input()
N = len(S)
mod13 = [0] * 13
mod13[0] = 1
exponent = 1
for i in range(1, N + 1):
    mod13_new = [0] * 13
    c = S[-i]
    if c == "?":
        for n in range(10):
            m = n * exponent % 13
            for r in range(13):
                mod13_new[(r + m) % 13] += mod13[r]
    else:
        for r in range(13):
            mod13_new[(r + int(c) * exponent) % 13] = mod13[r]
    exponent = exponent * 10 % 13
    for r in range(13):
        mod13_new[r] %= MOD
    mod13 = mod13_new
print(mod13[5])

Fixed submission:
def main():
    MOD = 10 ** 9 + 7
    S = input()
    N = len(S)
    mod13 = [[0] * 13 for _ in range(N + 1)]
    mod13[0][0] = 1
    exponent = 1
    for i in range(1, N + 1):
        c = S[-i]
        if c == "?":
            for n in range(10):
                m = n * exponent % 13
                for r in range(13):
                    mod13[i][(r + m) % 13] += mod13[i - 1][r]
        else:
            m = int(c) * exponent % 13
            for r in range(13):
                mod13[i][(r + m) % 13] = mod13[i - 1][r]
        exponent = exponent * 10 % 13
        for r in range(13):
            mod13[i][r] %= MOD
    print(mod13[N][5])

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
def main():
    MOD = 10 ** 9 + 7
    S = input()
    N = len(S)
    mod13 = [np.zeros((13,), dtype=np.int64) for _ in range(N + 1)]
    mod13[0][0] = 1
    exponent = 1
    for i in range(1, N + 1):
        c = S[-i]
        if c == "?":
            for n in range(10):
                m = n * exponent % 13
                mod13[i] += np.roll(mod13[i - 1], m)
        else:
            m = int(c) * exponent % 13
            mod13[i] += np.roll(mod13[i - 1], m)
        exponent = exponent * 10 % 13
        mod13[i] %= MOD
    print(mod13[N][5])

if __name__ == "__main__":
    main()

Fixed submission:
def main():
    MOD = 10 ** 9 + 7
    S = input()
    N = len(S)
    mod13 = [[0] * 13 for _ in range(N + 1)]
    mod13[0][0] = 1
    exponent = 1
    for i in range(1, N + 1):
        c = S[-i]
        if c == "?":
            for n in range(10):
                m = n * exponent % 13
                for r in range(13):
                    mod13[i][(r + m) % 13] += mod13[i - 1][r]
        else:
            m = int(c) * exponent % 13
            for r in range(13):
                mod13[i][(r + m) % 13] = mod13[i - 1][r]
        exponent = exponent * 10 % 13
        for r in range(13):
            mod13[i][r] %= MOD
    print(mod13[N][5])

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
MOD = 10 ** 9 + 7
S = input()
N = len(S)
mod13 = [np.zeros((13,), dtype=np.int64) for _ in range(N + 1)]
mod13[0][0] = 1
exponent = 1
for i in range(1, N + 1):
    c = S[-i]
    if c == "?":
        for n in range(10):
            m = n * exponent % 13
            mod13[i] += np.roll(mod13[i - 1], m)
    else:
        m = int(c) * exponent % 13
        mod13[i] += np.roll(mod13[i - 1], m)
    exponent = exponent * 10 % 13
    mod13[i] %= MOD
print(mod13[N][5])

Fixed submission:
def main():
    MOD = 10 ** 9 + 7
    S = input()
    N = len(S)
    mod13 = [[0] * 13 for _ in range(N + 1)]
    mod13[0][0] = 1
    exponent = 1
    for i in range(1, N + 1):
        c = S[-i]
        if c == "?":
            for n in range(10):
                m = n * exponent % 13
                for r in range(13):
                    mod13[i][(r + m) % 13] += mod13[i - 1][r]
        else:
            m = int(c) * exponent % 13
            for r in range(13):
                mod13[i][(r + m) % 13] = mod13[i - 1][r]
        exponent = exponent * 10 % 13
        for r in range(13):
            mod13[i][r] %= MOD
    print(mod13[N][5])

if __name__ == "__main__":
    main()