Xsquare loves to play with numbers a lot. Today, he has a multi set S consisting of N integer elements. At first, he has listed all the subsets of his multi set S and later replaced all the subsets with the maximum element present in the respective subset.

For example :

Consider the following multi set consisting of 3 elements S = {1,2,3}.

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Now, Xsquare wonders that given an integer K how many elements in the final list are greater than ( > ) , less than ( < ) or equals to ( == ) K.

To make this problem a bit more interesting, Xsquare decided to add Q queries to this problem. Each of the queries has one of the following type.

> K : Count the number of elements X in the final list such that X > K.
< K : Count the number of elements X in the final list such that X < K.
= K : Count the number of elements X in the final list such that X == K.

Note:

Answer to a particular query can be very large. Therefore, Print the required answer modulo 10⁹+7.
An empty subset is replaced by an integer 0.

Input

First line of input contains two space separated integers N and Q denoting the size of multiset S and number of queries respectively. Next line of input contains N space separated integers denoting elements of multi set S. Next Q lines of input contains Q queries each having one of the mentioned types.

Output

For each query, print the required answer modulo 10⁹+7.

Constraints:

1 ≤ N,Q ≤ 5*10⁵

1 ≤ K,S_i ≤ 10⁹

query_type = { < , > , = }

Warning :

Prefer to use printf / scanf instead of cin / cout.