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

# 下からi桁(1-indexed)まで使ったときの、13で割ったときあまりがjになるパターン
dp = [[0 for _ in range(13)] for _ in range(len(S)+1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1]):
    r_now = [1, 10, 9, 12, 3, 4][i%6]
    if s == "?":
        for d in range(10):
            for r_before, count in enumerate(dp[i]):
                j = (r_now*d+r_before)%13
                dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    else:
        d = int(s)
        for r_before, count in enumerate(dp[i]):
            j = (r_now*d+r_before)%13
            dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    # for dp_i in dp:
    #     print(dp_i)
    # print("")

print(dp[len(S)][5])

Fixed submission:
S = input()

# 下からi桁(1-indexed)まで使ったときの、13で割ったときあまりがjになるパターン
dp = [[0 for _ in range(13)] for _ in range(len(S)+1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1]):
    r_now = [1, 10, 9, 12, 3, 4][i%6]
    if s == "?":
        for d in range(10):
            for r_before, count in enumerate(dp[i]):
                j = (r_now*d+r_before)%13
                dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    else:
        d = int(s)
        for r_before, count in enumerate(dp[i]):
            j = (r_now*d+r_before)%13
            dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    # for dp_i in dp:
    #     print(dp_i)
    # print("")

print(dp[len(S)][5])

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

# 下からi桁(1-indexed)まで使ったときの、13で割ったときあまりがjになるパターン
dp = [[0 for _ in range(13)] for _ in range(len(S)+1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1]):
    r_now = [1, 10, 9, 12, 3, 4][i%6]
    if s == "?":
        for d in range(10):
            for r_before, count in enumerate(dp[i]):
                j = (r_now*d+r_before)%13
                dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    else:
        d = int(s)
        for r_before, count in enumerate(dp[i]):
            j = (r_now*d+r_before)%13
            dp[i+1][j] += (dp[i+1][j]+count)%(10**9+7)
    # for dp_i in dp:
    #     print(dp_i)
    # print("")

print(dp[len(S)][5])

Fixed submission:
S = input()

# 下からi桁(1-indexed)まで使ったときの、13で割ったときあまりがjになるパターン
dp = [[0 for _ in range(13)] for _ in range(len(S)+1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1]):
    r_now = [1, 10, 9, 12, 3, 4][i%6]
    if s == "?":
        for d in range(10):
            for r_before, count in enumerate(dp[i]):
                j = (r_now*d+r_before)%13
                dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    else:
        d = int(s)
        for r_before, count in enumerate(dp[i]):
            j = (r_now*d+r_before)%13
            dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    # for dp_i in dp:
    #     print(dp_i)
    # print("")

print(dp[len(S)][5])

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

# 下からi桁(1-indexed)まで使ったときの、13で割ったときあまりがjになるパターン
dp = [[0 for _ in range(13)] for _ in range(len(S)+1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1]):
    r_now = [1, 10, 9, 12, 3, 4][i%6]
    if s == "?":
        for d in range(10):
            for r_before, count in enumerate(dp[i]):
                j = (r_now*d+r_before)%13
                dp[i+1][j] += count 
    else:
        d = int(s)
        for r_before, count in enumerate(dp[i]):
            j = (r_now*d+r_before)%13
            dp[i+1][j] += count
    # for dp_i in dp:
    #     print(dp_i)
    # print("")

print(dp[len(S)][5]%(10**9+7))

Fixed submission:
S = input()

# 下からi桁(1-indexed)まで使ったときの、13で割ったときあまりがjになるパターン
dp = [[0 for _ in range(13)] for _ in range(len(S)+1)]
dp[0][0] = 1

for i, s in enumerate(S[::-1]):
    r_now = [1, 10, 9, 12, 3, 4][i%6]
    if s == "?":
        for d in range(10):
            for r_before, count in enumerate(dp[i]):
                j = (r_now*d+r_before)%13
                dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    else:
        d = int(s)
        for r_before, count in enumerate(dp[i]):
            j = (r_now*d+r_before)%13
            dp[i+1][j] = (dp[i+1][j]+count)%(10**9+7)
    # for dp_i in dp:
    #     print(dp_i)
    # print("")

print(dp[len(S)][5])