There are N people in a country and everyone needs to be given two doses of covid vaccination. The government provided two arrays X and Y, of length M.

*Xi denotes that exactly Xi people should be vaccinated with the first dose on the ith day of vaccination 
*Yi denotes that no more than Yi people should be vaccinated with the second dose on the ith day

It is given that if a person is vaccinated with the first dose on a jth day, then the second dose should be on day j or later.

Find the total no of ways in which government can assign day of two doses to each of the n people such that all the people are vaccinated in M days. Since the answer can be very large, return it modulo 10^9+7.

Note: It is given that the sum of all Xi is equal to N. Also it is guaranteed that Xi<=Yi

1<=N<=1000 1<=M<=100 0<=Xi<=100 0<=Yi<=100

Example: N 3 M 2 X-> 1,2 Y-> 2,2

OUTPUT=3