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:

<image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.math.BigInteger;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author tarek
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        HMateuszAndAnInfiniteSequence solver = new HMateuszAndAnInfiniteSequence();
        solver.solve(1, in, out);
        out.close();
    }

    static class HMateuszAndAnInfiniteSequence {
        long[] lens;
        Description[] cache;
        int m;
        int[] b;
        int[] gen;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int d = in.readInt();
            m = in.readInt();
            gen = new int[d];
            for (int i = 0; i < d; ++i) gen[i] = in.readInt();
            int blen = in.readInt();
            b = new int[blen];
            for (int i = 0; i < blen; ++i) {
                b[i] = in.readInt();
            }
            long left = in.readLong();
            long right = in.readLong();
            lens = new long[100];
            long len = 1;
            int layer = 0;
            lens[layer] = len;
            while (true) {
                ++layer;
                if (len < (right + d - 1) / d) {
                    len *= d;
                    lens[layer] = len;
                } else {
                    lens[layer] = right + 1;
                    break;
                }
            }
            cache = new Description[layer + 1];
            Description d1 = describe(layer, right);
            Description d2 = describe(layer, left + b.length - 2);
            long res = d1.matchesInside[0] - d2.matchesInside[0];
            out.printLine(res);
        }

        private Description describe(int layer, long upto) {
            if (upto > lens[layer]) throw new RuntimeException();
            if (upto == lens[layer]) {
                if (cache[layer] != null) return cache[layer];
            }
            Description res = null;
            if (upto <= 0) {
                res = new Description(upto);
                return res;
            }
            if (layer == 0) {
                res = new Description(upto);
                for (int shift = 0; shift < m; ++shift) {
                    if (b.length > 1 && b[0] >= shift) {
                        res.matchesPrefix[shift] = BigInteger.ONE;
                    } else {
                        res.matchesPrefix[shift] = BigInteger.ZERO;
                    }
                    if (b.length > 1 && b[b.length - 1] >= shift) {
                        res.matchesSuffix[shift] = BigInteger.ONE.shiftLeft(b.length - 1);
                    } else {
                        res.matchesSuffix[shift] = BigInteger.ZERO;
                    }
                    if (b.length == 1 && b[0] >= shift) {
                        ++res.matchesInside[shift];
                    }
                    byte[] bits = new byte[(b.length + 7) >> 3];
                    for (int i = 0; i < b.length; ++i) {
                        if (b[i] >= shift) {
                            bits[bits.length - 1 - (i >> 3)] |= (1 << (i & 7));
                        }
                    }
                    res.coveredIfStartsFrom[shift] = new BigInteger(1, bits);
                }
            } else {
                long togo = upto;
                for (int i = 0; i < gen.length && togo > 0; ++i) {
                    long by = Math.min(togo, lens[layer - 1]);
                    Description d = describe(layer - 1, by);
                    res = combine(res, d, gen[i]);
                    togo -= by;
                }
            }
            if (res == null) throw new RuntimeException();
            if (upto == lens[layer]) {
                cache[layer] = res;
            }
            return res;
        }

        private Description combine(Description a, Description b, int delta) {
            if (a == null) {
                if (delta != 0) throw new RuntimeException();
                return b;
            }
            Description res = new Description(a.len + b.len);
            for (int shift = 0; shift < m; ++shift) {
                int ashift = shift;
                int bshift = (shift + delta) % m;
                res.matchesInside[shift] = a.matchesInside[ashift] + b.matchesInside[bshift];
                res.matchesInside[shift] += a.matchesPrefix[ashift].and(b.matchesSuffix[bshift].shiftRight(1)).bitCount();
                res.matchesPrefix[shift] = b.matchesPrefix[bshift];
                if (b.len < this.b.length) {
                    res.matchesPrefix[shift] = res.matchesPrefix[shift].or(a.matchesPrefix[ashift].and(b.coveredIfStartsFrom[bshift].shiftRight(1)).shiftLeft((int) b.len));
                }
                res.matchesSuffix[shift] = a.matchesSuffix[ashift];
                if (a.len < this.b.length) {
                    res.matchesSuffix[shift] = res.matchesSuffix[shift].or(b.matchesSuffix[bshift].shiftRight((int) a.len).and(a.coveredIfStartsFrom[ashift]));
                }
                if (a.len < this.b.length) {
                    res.coveredIfStartsFrom[shift] = a.coveredIfStartsFrom[ashift].and(b.coveredIfStartsFrom[bshift].shiftRight((int) a.len));
                } else {
                    res.coveredIfStartsFrom[shift] = BigInteger.ZERO;
                }
            }
            return res;
        }

        class Description {
            long len;
            long[] matchesInside = new long[m];
            BigInteger[] matchesPrefix = new BigInteger[m];
            BigInteger[] matchesSuffix = new BigInteger[m];
            BigInteger[] coveredIfStartsFrom = new BigInteger[m];

            public Description(long len) {
                this.len = len;
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}