B'You have a set S of n distinct integers between 1 and m . Each second you do the following steps: What is the expected number of seconds until S is empty? Output the answer modulo 1 ,000 ,000 ,007 . Formally, let P = 1 ,000 ,000 ,007 . It can be shown that the answer can be expressed as an irreducible fraction frac{a}{b} , where a and b are integers and b not equiv 0 pmod{P} . Output the integer equal to a cdot b^{-1} bmod P . In other words, output an integer z such that 0 <= z < P and z cdot b equiv a pmod{P} . The first line contains two integers n and m ( 1 <= q n <= q m <= q 500 ) -- the number of elements in the set S and the upper bound on the value of the elements in S . The second line contains n integers S_1, ,S_2, , ... , ,S_n ( 1 <= q S_1 < S_2 < ldots < S_n <= q m ) -- the elements of the set S . Output a single integer -- the expected number of seconds until S is empty, modulo 1 ,000 ,000 ,007 . For test 1, here is a list of all the possible scenarios and their probabilities: Adding them up, we get frac{1}{2} cdot 4 + frac{1}{4} cdot 4 + frac{1}{4} cdot 3 = frac{15}{4} . We see that 750000009 cdot 4 equiv 15 pmod{1 ,000 ,000 ,007} . '...