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

N = len(S)
# dp = [[0 for _ in range(13)] for _ in range(N + 1)]
# dp[N][0] = 1 # i = N - 1のケースでうまくいくための処置

dp = [[0 for _ in range(13)] for _ in range(2)]
dp[0][0] = 1 # i = N - 1のケースでうまくいくための処置
r = 0

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み
    r = 1 - r  # dpの0行目と1行目を交互に使う
    if S[i] == '?':
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[r][(j + w * k) % 13] += dp[1 - r][j]
                if dp[r][(j + w * k) % 13] >= p:
                    dp[r][(j + w * k) % 13] -= p
    else:
        k = int(S[i])
        for j in range(13):
            dp[r][(j + w * k) % 13] = dp[1 - r][j]

    dp[1 - r] = [0] * 13

print(dp[r][5])


Fixed submission:
p = 10**9 + 7
S = input()
N = len(S)

dp = [[0 for _ in range(13)] for _ in range(2)]
dp[0][0] = 1 # i = N - 1のケースでうまくいくための処置
r = 0

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み
    r = 1 - r  # dpの0行目と1行目を交互に使う
    if S[i] == '?':
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[r][(j + w * k) % 13] += dp[1 - r][j]
                if dp[r][(j + w * k) % 13] >= p:
                    dp[r][(j + w * k) % 13] -= p
    else:
        k = int(S[i])
        for j in range(13):
            dp[r][(j + w * k) % 13] = dp[1 - r][j]

    dp[1 - r] = [0] * 13

print(dp[r][5])

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

N = len(S)
# dp = [[0 for _ in range(13)] for _ in range(N + 1)]
# dp[N][0] = 1 # i = N - 1のケースでうまくいくための処置

dp = [[0 for _ in range(13)] for _ in range(2)]
dp[0][0] = 1 # i = N - 1のケースでうまくいくための処置
r = 0

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み
    r = 1 - r  # dpの0行目と1行目を交互に使う
    if S[i] == '?':
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[r][(j + w * k) % 13] = (dp[r][(j + w * k) % 13] + dp[1 - r][j]) % p
    else:
        k = int(S[i])
        for j in range(13):
            dp[r][(j + w * k) % 13] = dp[1 - r][j]

    dp[1 - r] = [0] * 13

print(dp[r][5])

Fixed submission:
p = 10**9 + 7
S = input()
N = len(S)

dp = [[0 for _ in range(13)] for _ in range(2)]
dp[0][0] = 1 # i = N - 1のケースでうまくいくための処置
r = 0

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み
    r = 1 - r  # dpの0行目と1行目を交互に使う
    if S[i] == '?':
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[r][(j + w * k) % 13] += dp[1 - r][j]
                if dp[r][(j + w * k) % 13] >= p:
                    dp[r][(j + w * k) % 13] -= p
    else:
        k = int(S[i])
        for j in range(13):
            dp[r][(j + w * k) % 13] = dp[1 - r][j]

    dp[1 - r] = [0] * 13

print(dp[r][5])

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

N = len(S)
dp = [[0 for _ in range(13)] for _ in range(N + 1)]
dp[N][0] = 1 # i = N - 1のケースでうまくいくための処置

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み

    if S[i] is not '?':
        k = int(S[i])
        for j in range(13):
            dp[i][(j + w * k) % 13] = dp[i + 1][j]
    else:
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[i][(j + w * k) % 13] = (dp[i][(j + w * k) % 13] + dp[i + 1][j]) % p

print(dp[0][5])


Fixed submission:
p = 10**9 + 7
S = input()
N = len(S)

dp = [[0 for _ in range(13)] for _ in range(2)]
dp[0][0] = 1 # i = N - 1のケースでうまくいくための処置
r = 0

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み
    r = 1 - r  # dpの0行目と1行目を交互に使う
    if S[i] == '?':
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[r][(j + w * k) % 13] += dp[1 - r][j]
                if dp[r][(j + w * k) % 13] >= p:
                    dp[r][(j + w * k) % 13] -= p
    else:
        k = int(S[i])
        for j in range(13):
            dp[r][(j + w * k) % 13] = dp[1 - r][j]

    dp[1 - r] = [0] * 13

print(dp[r][5])

Buggy python submission (verdict: Runtime Error):
S = input()
p = 10**9 + 7

N = len(S)
dp = [[0 for _ in range(13)] for _ in range(N + 1)]
dp[N][0] = 1 # i = N - 1のケースでうまくいくための処置

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み

    if S[i] is not '?':
        k = int(S[i])
        for j in range(13):
            dp[i][(j + w * k) % 13] = dp[i + 1][j]
    else:
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[i][(j + w * k) % 13] = (dp[i][(j + w * k) % 13] + dp[i + 1][j]) % p

print(dp[0][5])


Fixed submission:
p = 10**9 + 7
S = input()
N = len(S)

dp = [[0 for _ in range(13)] for _ in range(2)]
dp[0][0] = 1 # i = N - 1のケースでうまくいくための処置
r = 0

for i in range(N - 1,  -1,  -1):  # 小さい桁から順に
    w = 1 if i == N - 1 else (w * 10) % 13 # 各桁の重み
    r = 1 - r  # dpの0行目と1行目を交互に使う
    if S[i] == '?':
        for j in range(13):
            for k in range(10): # ?の値が0, 1, ..., 9のとき
                dp[r][(j + w * k) % 13] += dp[1 - r][j]
                if dp[r][(j + w * k) % 13] >= p:
                    dp[r][(j + w * k) % 13] -= p
    else:
        k = int(S[i])
        for j in range(13):
            dp[r][(j + w * k) % 13] = dp[1 - r][j]

    dp[1 - r] = [0] * 13

print(dp[r][5])