Given two array A and B of length 5. You have 5 problems to solve in a contest. For $i^{th}$ problem you need exactly $A_i$ minutes to solve. But you can't concentrate on $i^{th}$ problem for more than $B_i$ minutes continuously. Find number of ways to schedule the $\sum_{i=1}^{5}A_i$ minutes so that you will solve all the 5 problems (mod $10^9 + 7$)? Scheduling means for each minute, you have to decide on which problem you will concentrate during that minute.

Two schedules are considered different if at-least for one of the $\sum_{i=1}^{5}A_i$ minutes, you are concentrating on different problems in both the schedules.

Input Format:
First line contains 5 space separated integers, denoting $A_i$ $(1 \le A_i \le 10)$. Second line contains 5 space separated integers, denoting $B_i$ $(1 \le B_i \le 10)$.

Output Format:
Find number of ways to schedule the $\sum_{i=1}^{5}A_i$ minutes so that you will solve all the 5 problems (mod $10^9 + 7$)