Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
MOD = 10**9 + 7
def solve(s, p=13):
    s = s[::-1]
    n = len(s)
    a = np.zeros(p, dtype=int)
    b = np.zeros(p, dtype=int)
    if s[0] == "?":
        a[:10] = 1
    else:
        a[int(s[0])] = 1
    D = {str(i): [i] for i in range(10)}
    D["?"] = list(range(10))
    q = [(10**i) % p for i in range(6)]
    for i in range(1,n):
        b[:] = 0
        for s_i in D[s[i]]:
            for j in range(p):
                k = (j + s_i * q[i%6]) % p
                b[k] += a[j]
        a = b % MOD
    return a[5]

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

Fixed submission:
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))

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
MOD = 10**9 + 7
def solve(s, p=13):
    s = s[::-1]
    n = len(s)
    cur = np.zeros(p, dtype=np.uint64)
    if s[0] == "?":
        cur[:10] = 1
    else:
        cur[int(s[0])] = 1
    D = {str(i): [i] for i in range(10)}
    D["?"] = list(range(10))
    q = [(10**i) % p for i in range(6)]
    for i in range(1,n):
        next = np.zeros(p, dtype=np.uint64)
        for x in D[s[i]]:
            for j in range(p):
                k = (j + x * q[i%6]) % p
                next[k] += cur[j]
        cur = next % MOD
    return cur[5]

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

Fixed submission:
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))

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
MOD = 10**9 + 7
def solve(s, p=13):
    s = s[::-1]
    n = len(s)
    dp = np.zeros((n, p), dtype=int)
    if s[0] == "?":
        dp[0, :10] = 1
    else:
        dp[0, int(s[0])] = 1
    D = {str(i): [i] for i in range(10)}
    D["?"] = list(range(10))
    q = [(10**i) % p for i in range(6)]
    for i in range(1,n):
        for x in D[s[i]]:
            for j in range(p):
                k = (j + x * q[i%6]) % p
                dp[i, k] = (dp[i, k] + dp[i-1, j]) % MOD
    return dp[n-1, 5]

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

Fixed submission:
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))

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
MOD = 10**9 + 7
def solve(s, p=13):
    s = s[::-1]
    n = len(s)
    dp = np.zeros((n, p), dtype=int)
    if s[0] == "?":
        dp[0, :10] = 1
    else:
        dp[0, int(s[0])] = 1
    for i in range(1,n):
        if s[i] == "?":
            v = list(range(10))
        else:
            v = [int(s[i])]
        for x in v:
            for j in range(p):
                k = (j + x * (10**i)) % p
                dp[i, k] = (dp[i, k] + dp[i-1, j]) % MOD
    return dp[n-1, 5]

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

Fixed submission:
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))