Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
MOD = 10 ** 9 + 7

# dp[i][j] := i文字目までみた時に13で割ってj余るような数の通り数
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S):
    for j in range(13):
        if s != '?':
            dp[i + 1][((j * 10) + int(s)) % 13] += dp[i][j]
            dp[i + 1][((j * 10) + int(s)) % 13] %= MOD
        else:
            for k in range(10):
                dp[i + 1][((j * 10) + k) % 13] += dp[i][j]
                dp[i + 1][((j * 10) + k) % 13] %= MOD

print(dp[-1][5] % MOD)


Fixed submission:
S = input()
N = len(S)
MOD = 10 ** 9 + 7
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1], start=1):
    p10 = pow(10, i - 1, 13)
    if s != '?':
        for k in range(13):
            dp[i][(int(s) * p10 + k) % 13] += dp[i - 1][k]
            dp[i][(int(s) * p10 + k) % 13] %= MOD
    else:
        for j in range(10):
            for k in range(13):
                dp[i][(j * p10 + k) % 13] += dp[i - 1][k]
                dp[i][(j * p10 + k) % 13] %= MOD

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

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
MOD = 10 ** 9 + 7

# dp[i][j] := i文字目までみた時に13で割ってj余るような数の通り数
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S):
    for j in range(13):
        if s != '?':
            dp[i + 1][((j * 10) + int(s)) % 13] += dp[i][j]
            dp[i + 1][((j * 10) + int(s)) % 13] %= MOD
        else:
            for k in range(10):
                dp[i + 1][((j * 10) + k) % 13] += dp[i][j]
                dp[i + 1][((j * 10) + k) % 13] %= MOD

print(dp[-1][5] % MOD)


Fixed submission:
S = input()
N = len(S)
MOD = 10 ** 9 + 7
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1], start=1):
    p10 = pow(10, i - 1, 13)
    if s != '?':
        for k in range(13):
            dp[i][(int(s) * p10 + k) % 13] += dp[i - 1][k]
            dp[i][(int(s) * p10 + k) % 13] %= MOD
    else:
        for j in range(10):
            for k in range(13):
                dp[i][(j * p10 + k) % 13] += dp[i - 1][k]
                dp[i][(j * p10 + k) % 13] %= MOD

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

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
MOD = 10 ** 9 + 7
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

p10 = 1
for i, s in enumerate(S[::-1], start=1):
    if s != '?':
        for k in range(13):
            dp[i][(int(s) * p10 + k) % 13] += dp[i - 1][k]
            dp[i][(int(s) * p10 + k) % 13] %= MOD
    else:
        for j in range(10):
            for k in range(13):
                dp[i][(j * p10 + k) % 13] += dp[i - 1][k]
                dp[i][(j * p10 + k) % 13] %= MOD
    p10 *= 10
print(dp[N][5] % MOD)


Fixed submission:
S = input()
N = len(S)
MOD = 10 ** 9 + 7
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1], start=1):
    p10 = pow(10, i - 1, 13)
    if s != '?':
        for k in range(13):
            dp[i][(int(s) * p10 + k) % 13] += dp[i - 1][k]
            dp[i][(int(s) * p10 + k) % 13] %= MOD
    else:
        for j in range(10):
            for k in range(13):
                dp[i][(j * p10 + k) % 13] += dp[i - 1][k]
                dp[i][(j * p10 + k) % 13] %= MOD

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

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
MOD = 10 ** 9 + 7
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1], start=1):
    p10 = 10 ** (i - 1)
    if s != '?':
        for k in range(13):
            dp[i][(int(s) * p10 + k) % 13] += dp[i - 1][k]
            dp[i][(int(s) * p10 + k) % 13] %= MOD
    else:
        for j in range(10):
            for k in range(13):
                dp[i][(j * p10 + k) % 13] += dp[i - 1][k]
                dp[i][(j * p10 + k) % 13] %= MOD

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


Fixed submission:
S = input()
N = len(S)
MOD = 10 ** 9 + 7
dp = [[0] * 13 for i in range(N + 1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1], start=1):
    p10 = pow(10, i - 1, 13)
    if s != '?':
        for k in range(13):
            dp[i][(int(s) * p10 + k) % 13] += dp[i - 1][k]
            dp[i][(int(s) * p10 + k) % 13] %= MOD
    else:
        for j in range(10):
            for k in range(13):
                dp[i][(j * p10 + k) % 13] += dp[i - 1][k]
                dp[i][(j * p10 + k) % 13] %= MOD

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