Bob had a string S of length N which consists of letters from A to B both included. Q operational need to be performed on this string . It is given that in the ith operation the capitalization of characters from L[i] to R[i] will be flipped. This means that upon being flipped x becomes X and X becomes x if it was present in the range L[i] , R [ i] . After performing all the operations bob finds the length of the longest substring of the string that contains only capital letters . If this length is equal to REQ , he calls the initial string S s good string
Given a value of N , you need to find the total number of possible initial good strings . Since the answer can be very large return the answer modulo 10^9+7.
Note:
It is guaranteed that L[i] <= R[i] for all values of i
2). Lettera in the initial string may or may not be capitalized