B'Childan is making up a legendary story and trying to sell his forgery -- a necklace with a strong sense of "Wu" to the Kasouras. But Mr. Kasoura is challenging the truth of Childan 's story. So he is going to ask a few questions about Childan 's so-called "personal treasure" necklace. This "personal treasure" is a multiset S of m "01-strings". A "01-string" is a string that contains n characters "0" and "1". For example, if n=4 , strings "0110", "0000", and "1110" are "01-strings", but "00110" (there are 5 characters, not 4 ) and "zero" (unallowed characters) are not. Note that the multiset S can contain equal elements. Frequently, Mr. Kasoura will provide a "01-string" t and ask Childan how many strings s are in the multiset S such that the "Wu" value of the pair (s, t) is not greater than k . Mrs. Kasoura and Mr. Kasoura think that if s_i = t_i ( 1 <= q i <= q n ) then the "Wu" value of the character pair equals to w_i , otherwise 0 . The "Wu" value of the "01-string" pair is the sum of the "Wu" values of every character pair. Note that the length of every "01-string" is equal to n . For example, if w=[4, 5, 3, 6] , "Wu" of ("1001", "1100") is 7 because these strings have equal characters only on the first and third positions, so w_1+w_3=4+3=7 . You need to help Childan to answer Mr. Kasoura 's queries. That is to find the number of strings in the multiset S such that the "Wu" value of the pair is not greater than k . The first line contains three integers n , m , and q ( 1 <= q n <= q 12 , 1 <= q q, m <= q 5 cdot 10^5 ) -- the length of the "01-strings", the size of the multiset S , and the number of queries. The second line contains n integers w_1, w_2, ldots, w_n ( 0 <= w_i <= 100 ) -- the value of the i -th caracter. Each of the next m lines contains the "01-string" s '...