There is an old country and the king fell in love with a devil. The devil always asks the king to do some crazy things. Although the king used to be wise and beloved by his people. Now he is just like a boy in love and can’t refuse any request from the devil. Also, this devil is looking like a very cute Loli.
Y*wan still remember the day he first meets the devil. Now everything is done and the devil is gone. Y*wan feel very sad and suicide.
You feel guilty after killing so many loli, so you suicide too.
Nobody survive in this silly story, but there is still some hope, because this is just a silly background story during one programming contest!
And the last problem is:
Given a sequence a_1,a_2,...,a_n, if we can take some of them(each a_i can only be used once), and they sum to k, then we say this sequence is a good sequence.
How many good sequence are there? Given that each a_i is an integer and 0<= a_i <= L.
You should output the result modulo 10^9+7.