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