Buggy python submission (verdict: Time Limit Exceeded):
S = input()

MOD=(10**9) + 7
N=13

dp=[[0 for i in range(N)] for j in range(100005)]
dp[0][0] = 1

dpi = 1
mul = 1
for c in S[::-1]:    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (int(j)*mul)) % N
                dp[dpi][ii] += dp[dpi-1][i] % MOD
        else:
            ii = (i + (int(c)*mul)) % N
            dp[dpi][ii] += dp[dpi-1][i] % MOD
    mul *= 10
    dpi += 1

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

Fixed submission:
S = input()

MOD=(10**9) + 7
N=13

dp=[[0 for i in range(N)] for j in range(100005)]
dp[0][0] = 1

dpi = 1
mul = 1

for c in S[::-1]:    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (j*mul)) % N
                dp[dpi][ii] += dp[dpi-1][i] % MOD
                #pass
        else:
            j = int(c)
            ii = (i + (j*mul)) % N
            dp[dpi][ii] += dp[dpi-1][i] % MOD
            #pass
    mul *= 10
    mul %= N
    dpi += 1

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

Buggy python submission (verdict: Time Limit Exceeded):
S = input()

MOD=(10**9) + 7
N=13

dp=[0]*N
dp[0] = 1

mul = 1
for c in S[::-1]:
    next_dp=[0]*N
    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (int(j)*mul)) % N
                next_dp[ii] += dp[i]
                next_dp[ii] = next_dp[ii] % MOD
        else:
            ii = (i + (int(c)*mul)) % N
            next_dp[ii] += dp[i]
            next_dp[ii] = next_dp[ii] % MOD

    mul *= 10
    dp = next_dp

print(dp[5])

Fixed submission:
S = input()

MOD=(10**9) + 7
N=13

dp=[[0 for i in range(N)] for j in range(100005)]
dp[0][0] = 1

dpi = 1
mul = 1

for c in S[::-1]:    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (j*mul)) % N
                dp[dpi][ii] += dp[dpi-1][i] % MOD
                #pass
        else:
            j = int(c)
            ii = (i + (j*mul)) % N
            dp[dpi][ii] += dp[dpi-1][i] % MOD
            #pass
    mul *= 10
    mul %= N
    dpi += 1

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

Buggy python submission (verdict: Time Limit Exceeded):
S = input()

MOD=(10**9) + 7
N=13

dp=[0]*N
dp[0] = 1

mul = 1
for c in S[::-1]:
    next_dp=[0]*N
    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (int(j)*mul)) % N
                next_dp[ii] += dp[i]
                next_dp[ii] = next_dp[ii] % MOD
        else:
            ii = (i + (int(c)*mul)) % N
            next_dp[ii] += dp[i]
            next_dp[ii] = next_dp[ii] % MOD

    mul *= 10
    dp = next_dp

print(dp[5])

Fixed submission:
S = input()

MOD=(10**9) + 7
N=13

dp=[[0 for i in range(N)] for j in range(100005)]
dp[0][0] = 1

dpi = 1
mul = 1

for c in S[::-1]:    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (j*mul)) % N
                dp[dpi][ii] += dp[dpi-1][i] % MOD
                #pass
        else:
            j = int(c)
            ii = (i + (j*mul)) % N
            dp[dpi][ii] += dp[dpi-1][i] % MOD
            #pass
    mul *= 10
    mul %= N
    dpi += 1

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