H. Mateusz and an Infinite Sequencetime limit per test7 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA Thue-Morse-Radecki-Mateusz sequence (Thorse-Radewoosh sequence in short) is an infinite sequence constructed from a finite sequence \mathrm{gen} of length d and an integer m, obtained in the following sequence of steps:  In the beginning, we define the one-element sequence M_0=(0). In the k-th step, k \geq 1, we define the sequence M_k to be the concatenation of the d copies of M_{k-1}. However, each of them is altered slightly — in the i-th of them (1 \leq i \leq d), each element x is changed to (x+\mathrm{gen}_i) \pmod{m}. For instance, if we pick \mathrm{gen} = (0, \color{blue}{1}, \color{green}{2}) and m = 4:   M_0 = (0),  M_1 = (0, \color{blue}{1}, \color{green}{2}),  M_2 = (0, 1, 2, \color{blue}{1, 2, 3}, \color{green}{2, 3, 0}),  M_3 = (0, 1, 2, 1, 2, 3, 2, 3, 0, \color{blue}{1, 2, 3, 2, 3, 0, 3, 0, 1}, \color{green}{2, 3, 0, 3, 0, 1, 0, 1, 2}), and so on. As you can see, as long as the first element of \mathrm{gen} is 0, each consecutive step produces a sequence whose prefix is the sequence generated in the previous step. Therefore, we can define the infinite Thorse-Radewoosh sequence M_\infty as the sequence obtained by applying the step above indefinitely. For the parameters above, M_\infty = (0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, \dots).Mateusz picked a sequence \mathrm{gen} and an integer m, and used them to obtain a Thorse-Radewoosh sequence M_\infty. He then picked two integers l, r, and wrote down a subsequence of this sequence A := ((M_\infty)_l, (M_\infty)_{l+1}, \dots, (M_\infty)_r).Note that we use the 1-based indexing both for M_\infty and A.Mateusz has his favorite sequence B with length n, and would like to see how large it is compared to A. Let's say that B majorizes sequence X of length n (let's denote it as B \geq X) if and only if for all i \in \{1, 2, \dots, n\}, we have B_i \geq X_i.He now asks himself how many integers x in the range [1, |A| - n + 1] there are such that B \geq (A_x, A_{x+1}, A_{x+2}, \dots, A_{x+n-1}). As both sequences were huge, answering the question using only his pen and paper turned out to be too time-consuming. Can you help him automate his research?InputThe first line contains two integers d and m (2 \leq d \leq 20, 2 \leq m \leq 60) — the length of the sequence \mathrm{gen} and an integer used to perform the modular operations. The second line contains d integers \mathrm{gen}_i (0 \leq \mathrm{gen}_i < m). It's guaranteed that the first element of the sequence \mathrm{gen} is equal to zero.The third line contains one integer n (1 \leq n \leq 30000) — the length of the sequence B. The fourth line contains n integers B_i (0 \leq B_i < m). The fifth line contains two integers l and r (1 \leq l \leq r \leq 10^{18}, r-l+1 \geq n).OutputPrint a single integer — the answer to the problem.ExamplesInput
2 2
0 1
4
0 1 1 0
2 21
Output
6
Input
3 4
0 1 2
2
0 2
6 11
Output
1
NoteThorse-Radewoosh sequence in the first example is the standard Thue-Morse sequence, so the sequence A is as follows: 11010011001011010010. Here are the places where the sequence B majorizes A:  
2 2
0 1
4
0 1 1 0
2 21

6 
['bitmasks', 'brute force', 'dp', 'strings', '*3400']