Buggy python submission (verdict: Time Limit Exceeded):
S=input()
N=len(S)
mod=13
mod2=10**9+7

#i桁目までみて，あまりがjになるものの個数
dp=[[0]*mod for _ in range(N+1)]

#1桁目
if S[-1]!="?":
    a=int(S[-1])
    for j in range(mod):
        dp[1][a]=1
else:
    for j in range(mod):
        for k in range(10):
            dp[1][k]=1

for i in range(1,N):
    if S[-i-1]!="?":
        a=(pow(10,i)*int(S[-i-1]))%mod
        for j in range(mod):
            dp[i+1][(j+a)%mod]=dp[i][j]
    else:
        a=pow(10,i)%mod
        for j in range(mod):
            for k in range(10):
                dp[i+1][(j+k*a)%mod]+=dp[i][j]
                dp[i+1][(j+k*a)%mod]%=mod2

print(dp[-1][5])

Fixed submission:
S=input()
N=len(S)
mod=13
mod2=10**9+7

#上からi桁目までみて，あまりがjになるものの個数
dp=[[0]*mod for _ in range(N+1)]

dp[0][0]=1

for i in range(N):
    if S[i]!="?":
        for j in range(mod):
            dp[i+1][(10*j+int(S[i]))%mod]=dp[i][j]
    else:
        for j in range(mod):
            for k in range(10):
                dp[i+1][(10*j+k)%mod]+=dp[i][j]%mod2

print(dp[-1][5]%mod2)

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

S=input()
N=len(S)
mod=13
mod2=10**9+7

#i桁目までみて，あまりがjになるものの個数
dp=[[0]*mod for _ in range(N+1)]

#1桁目
if S[-1]!="?":
    a=int(S[-1])
    for j in range(mod):
        dp[1][a]=1
else:
    for j in range(mod):
        for k in range(10):
            dp[1][k]=1

for i in range(1,N):
    if S[-i-1]!="?":
        a=(pow(10,i)*int(S[-i-1]))%mod
        for j in range(mod):
            dp[i+1][(j+a)%mod]=dp[i][j]
    else:
        a=pow(10,i)%mod
        for j in range(mod):
            for k in range(10):
                dp[i+1][(j+k*a)%mod]+=dp[i][j]
                dp[i+1][(j+k*a)%mod]%=mod2

print(dp[-1][5])

Fixed submission:
S=input()
N=len(S)
mod=13
mod2=10**9+7

#上からi桁目までみて，あまりがjになるものの個数
dp=[[0]*mod for _ in range(N+1)]

dp[0][0]=1

for i in range(N):
    if S[i]!="?":
        for j in range(mod):
            dp[i+1][(10*j+int(S[i]))%mod]=dp[i][j]
    else:
        for j in range(mod):
            for k in range(10):
                dp[i+1][(10*j+k)%mod]+=dp[i][j]%mod2

print(dp[-1][5]%mod2)

Buggy python submission (verdict: Time Limit Exceeded):
S=input()
N=len(S)
mod=13
mod2=10**9+7

#i桁目までみて，あまりがjになるものの個数
dp=[[0]*mod for _ in range(N+1)]

#1桁目
if S[-1]!="?":
    a=int(S[-1])
    for j in range(mod):
        dp[1][a]=1
else:
    for j in range(mod):
        for k in range(10):
            dp[1][k]=1

for i in range(1,N):
    if S[-i-1]!="?":
        a=(pow(10,i)*int(S[-i-1]))%mod
        for j in range(mod):
            dp[i+1][(j+a)%mod]=dp[i][j]
    else:
        a=pow(10,i)%mod
        for j in range(mod):
            for k in range(10):
                dp[i+1][(j+k*a)%mod]+=dp[i][j]
                dp[i+1][(j+k*a)%mod]%=mod2

print(dp[-1][5])

Fixed submission:
S=input()
N=len(S)
mod=13
mod2=10**9+7

#上からi桁目までみて，あまりがjになるものの個数
dp=[[0]*mod for _ in range(N+1)]

dp[0][0]=1

for i in range(N):
    if S[i]!="?":
        for j in range(mod):
            dp[i+1][(10*j+int(S[i]))%mod]=dp[i][j]
    else:
        for j in range(mod):
            for k in range(10):
                dp[i+1][(10*j+k)%mod]+=dp[i][j]%mod2

print(dp[-1][5]%mod2)