Buggy python submission (verdict: Time Limit Exceeded):
s = input()
n = len(s)
mod = 10**9 + 7
dp = [[0 for i in range(n)] for j in range(13)]

if s[0] == '?':
    for i in range(10):
        dp[i][0] = 1
else:
    dp[int(s[0])][0] = 1

mod_change_table = [(i*10)%13 for i in range(13)]

for x in range(1,len(s)):
    for y in range(13):
        if s[x]=='?':
            for j in range(10):
                dp[(mod_change_table[y]+j)%13][x] += dp[y][x-1]
        else:
            dp[(mod_change_table[y]+int(s[x]))%13][x] += dp[y][x-1]
            

print(dp[5][n-1] % mod)

Fixed submission:
s = input()
mod = 10**9+7

# dp[逆順i桁][j mod 13] := 総数
dp = [[0]*13 for _ in range(len(s)+1)]
dp[0][0] = 1
mul = 1
s_rev = s[::-1]
for i in range(len(s)):
    x = s_rev[i]
    if x == '?':
        for k in range(10):
            for j in range(13):
                dp[i+1][(mul*k+j)%13] += dp[i][j]
                dp[i+1][(mul*k+j)%13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i+1][(mul*k+j)%13] += dp[i][j]
            dp[i+1][(mul*k+j)%13] %= mod
    mul = mul * 10 % 13

print(dp[len(s)][5] % mod)

Buggy python submission (verdict: Time Limit Exceeded):
s = input()
n = len(s)
mod = 10**9 + 7
dp = [[0 for i in range(n)] for j in range(13)]

if s[0] == '?':
    for i in range(10):
        dp[i][0] = 1
else:
    dp[int(s[0])][0] = 1

mod_change_table = [(i*10)%13 for i in range(13)]

for x in range(1,len(s)):
    for y in range(13):
        if s[x]=='?':
            for j in range(10):
                dp[(mod_change_table[y]+j)%13][x] += dp[y][x-1]
        else:
            dp[(mod_change_table[y]+int(s[x]))%13][x] += dp[y][x-1]
            

print(dp[5][n-1] % mod)

Fixed submission:
s = input()
mod = 10**9+7

# dp[逆順i桁][j mod 13] := 総数
dp = [[0]*13 for _ in range(len(s)+1)]
dp[0][0] = 1
mul = 1
s_rev = s[::-1]
for i in range(len(s)):
    x = s_rev[i]
    if x == '?':
        for k in range(10):
            for j in range(13):
                dp[i+1][(mul*k+j)%13] += dp[i][j]
                dp[i+1][(mul*k+j)%13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i+1][(mul*k+j)%13] += dp[i][j]
            dp[i+1][(mul*k+j)%13] %= mod
    mul = mul * 10 % 13

print(dp[len(s)][5] % mod)

Buggy python submission (verdict: Time Limit Exceeded):
s = input()
n = len(s)
mod = 10**9 + 7
dp = [[0 for i in range(n)] for j in range(13)]

if s[0] == '?':
    for i in range(10):
        dp[i][0] = 1
else:
    dp[int(s[0])][0] = 1

mod_change_table = [(i*10)%13 for i in range(13)]

for x in range(1,len(s)):
    for y in range(13):
        if s[x]=='?':
            for j in range(10):
                dp[(mod_change_table[y]+j)%13][x] += dp[y][x-1]
        else:
            dp[(mod_change_table[y]+int(s[x]))%13][x] += dp[y][x-1]
            

print(dp[5][n-1] % mod)

Fixed submission:
s = input()
mod = 10**9+7

# dp[逆順i桁][j mod 13] := 総数
dp = [[0]*13 for _ in range(len(s)+1)]
dp[0][0] = 1
mul = 1
s_rev = s[::-1]
for i in range(len(s)):
    x = s_rev[i]
    if x == '?':
        for k in range(10):
            for j in range(13):
                dp[i+1][(mul*k+j)%13] += dp[i][j]
                dp[i+1][(mul*k+j)%13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i+1][(mul*k+j)%13] += dp[i][j]
            dp[i+1][(mul*k+j)%13] %= mod
    mul = mul * 10 % 13

print(dp[len(s)][5] % mod)

Buggy python submission (verdict: Runtime Error):
s = input()
n = len(s)
mod = 10**9 + 7
dp = [[0 for i in range(n)] for j in range(13)]

if s[0] == '?':
    for i in range(10):
        dp[i][0] = 1
else:
    dp[s][0] = 1

mod_change_table = [(i*10)%13 for i in range(13)]

for x in range(1,len(s)):
    for y in range(13):
        if s[x]=='?':
            for j in range(10):
                dp[(mod_change_table[y]+j)%13][x] += dp[y][x-1]
        else:
            dp[(mod_change_table[y]+int(s[x]))%13][x] += dp[y][x-1]
            

print(dp[5][n-1] % mod)

Fixed submission:
s = input()
mod = 10**9+7

# dp[逆順i桁][j mod 13] := 総数
dp = [[0]*13 for _ in range(len(s)+1)]
dp[0][0] = 1
mul = 1
s_rev = s[::-1]
for i in range(len(s)):
    x = s_rev[i]
    if x == '?':
        for k in range(10):
            for j in range(13):
                dp[i+1][(mul*k+j)%13] += dp[i][j]
                dp[i+1][(mul*k+j)%13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i+1][(mul*k+j)%13] += dp[i][j]
            dp[i+1][(mul*k+j)%13] %= mod
    mul = mul * 10 % 13

print(dp[len(s)][5] % mod)