Problem: A Thue-Morse-Radecki-Mateusz sequence (Thorse-Radewoosh sequence in short) is an infinite sequence constructed from a finite sequence 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 ≥ 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 ≤ i ≤ d), each element x is changed to (x+gen_i) \pmod{m}. 



For instance, if we pick 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 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_∞ as the sequence obtained by applying the step above indefinitely. For the parameters above, M_∞ = (0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, ...).

Mateusz picked a sequence gen and an integer m, and used them to obtain a Thorse-Radewoosh sequence M_∞. He then picked two integers l, r, and wrote down a subsequence of this sequence A := ((M_∞)_l, (M_∞)_{l+1}, ..., (M_∞)_r).

Note that we use the 1-based indexing both for M_∞ 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 ≥ X) if and only if for all i ∈ \{1, 2, ..., n\}, we have B_i ≥ X_i.

He now asks himself how many integers x in the range [1, |A| - n + 1] there are such that B ≥ (A_x, A_{x+1}, A_{x+2}, ..., 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?

Input

The first line contains two integers d and m (2 ≤ d ≤ 20, 2 ≤ m ≤ 60) — the length of the sequence gen and an integer used to perform the modular operations. The second line contains d integers gen_i (0 ≤ gen_i < m). It's guaranteed that the first element of the sequence gen is equal to zero.

The third line contains one integer n (1 ≤ n ≤ 30000) — the length of the sequence B. The fourth line contains n integers B_i (0 ≤ B_i < m). The fifth line contains two integers l and r (1 ≤ l ≤ r ≤ 10^{18}, r-l+1 ≥ n).

Output

Print a single integer — the answer to the problem.

Examples

Input


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

Note

Thorse-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:

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 30005;
int d, m, n, lm, i, j, b[N], gen[25];
long long L, R;
struct atom {
  bitset<N> pr, sf, all;
  long long ans, l;
  void set(int v) {
    if (v <= b[n]) pr.set(n);
    if (v <= b[1]) sf.set(1);
    for (int i = 1; i <= n; ++i)
      if (v <= b[i]) all.set(i);
    ans = n == 1 && v <= b[1];
    l = 1;
  }
} a[65][65];
inline atom uni(const atom& a, const atom& b) {
  static atom ret;
  ret.l = a.l + b.l;
  ret.pr = a.pr;
  if (a.l < n) ret.pr |= (a.all << a.l & b.pr) >> a.l;
  ret.sf = b.sf;
  if (b.l < n) ret.sf |= (b.all >> 1 & a.sf) << b.l;
  if (a.l + b.l <= n)
    ret.all = b.all >> a.l & a.all;
  else
    ret.all.reset();
  ret.ans = a.ans + b.ans + (a.sf << 1 & b.pr).count();
  return ret;
}
inline long long calc(long long x) {
  long long y = 0, pr = 0;
  static atom ans;
  bool fl = 0;
  ans.ans = 0;
  for (i = lm - 1; i >= 0; --i) {
    for (j = 0; y + a[i][(pr + gen[j]) % m].l <= x; ++j) {
      if (!fl)
        ans = a[i][(pr + gen[j]) % m], fl = 1;
      else
        ans = uni(ans, a[i][(pr + gen[j]) % m]);
      y += a[i][(pr + gen[j]) % m].l;
    }
    pr = (pr + gen[j]) % m;
  }
  return ans.ans;
}
int main() {
  scanf("%d%d", &d, &m);
  for (i = 0; i < d; ++i) scanf("%d", gen + i);
  scanf("%d", &n);
  for (i = 1; i <= n; ++i) scanf("%d", b + i);
  scanf("%lld%lld", &L, &R);
  for (i = 0; i < m; ++i) a[0][i].set(i);
  for (lm = 1; a[lm - 1][0].l <= R / d; ++lm)
    for (i = 0; i < m; ++i) {
      a[lm][i] = a[lm - 1][(i + gen[0]) % m];
      for (j = 1; j < d; ++j)
        a[lm][i] = uni(a[lm][i], a[lm - 1][(i + gen[j]) % m]);
    }
  printf("%lld\n", calc(R) - calc(L + n - 2));
  return 0;
}