Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.

You are given geometric progression b defined by two integers b1 and q. Remind that a geometric progression is a sequence of integers b1, b2, b3, ..., where for each i > 1 the respective term satisfies the condition bi = bi - 1·q, where q is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both b1 and q can equal 0. Also, Dvastan gave Masha m "bad" integers a1, a2, ..., am, and an integer l.

Masha writes all progression terms one by one onto the board (including repetitive) while condition |bi| ≤ l is satisfied (|x| means absolute value of x). There is an exception: if a term equals one of the "bad" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.

But the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print "inf" in case she needs to write infinitely many integers.

Input

The first line of input contains four integers b1, q, l, m (-109 ≤ b1, q ≤ 109, 1 ≤ l ≤ 109, 1 ≤ m ≤ 105) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of "bad" integers, respectively.

The second line contains m distinct integers a1, a2, ..., am (-109 ≤ ai ≤ 109) — numbers that will never be written on the board.

Output

Print the only integer, meaning the number of progression terms that will be written on the board if it is finite, or "inf" (without quotes) otherwise.

Examples

Input

3 2 30 4
6 14 25 48


Output

3

Input

123 1 2143435 4
123 11 -5453 141245


Output

0

Input

123 1 2143435 4
54343 -13 6 124


Output

inf

Note

In the first sample case, Masha will write integers 3, 12, 24. Progression term 6 will be skipped because it is a "bad" integer. Terms bigger than 24 won't be written because they exceed l by absolute value.

In the second case, Masha won't write any number because all terms are equal 123 and this is a "bad" integer.

In the third case, Masha will write infinitely integers 123. 
import java.io.*;
import java.util.*;

public final class Main {
    static char[] chars = {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'};
    static char[] chars1 = {'#', '*', '&'};
    static char[] chars2 = {'1', '2', '3', '4', '5', '6', '7', '8', '9', '0'};


    public void solve() {
        long b = in.nextInt();
        long q = in.nextInt();
        int l = in.nextInt();
        int m = in.nextInt();
        if (l < Math.abs(b)) {
            out.println(0);
            return;
        }
        TreeSet<Long> pq = new TreeSet<Long>();
        boolean qb = q > 0;
        for (int i = 0; i < m; i++) {
            pq.add(in.nextLong());
        }
        if (b == 0) {
            if (pq.contains(b)) {
                out.println(0);
            } else {
                out.println("inf");
            }
            return;
        }
        if (q == 0) {
            boolean bc = pq.contains(b);
            boolean b0 = pq.contains(0L);
            if (!b0) {
                out.println("inf");
                return;
            }
            if (!bc) {
                out.println("1");
                return;
            }
            out.println("0");
            return;
        }
        if (q == 1) {
            if (pq.contains(b)) {
                out.println(0L);
            } else {
                out.println("inf");
            }
            return;
        }
        if (q == -1) {
            boolean bc = pq.contains(b);
            boolean b0 = pq.contains(-b);
            if (!bc) {
                out.println("inf");
                return;
            }
            if (!b0) {
                out.println("inf");
                return;
            }
            out.println(0);
            return;
        }
        long ans = 0;
        while (Math.abs(b) <= l) {
            pq.add(b);
            b *= q;
        }
        out.println(pq.size()-m);
    }


    static class Library {
        static boolean isPrime(int a) {
            if (a == 1) {
                return false;
            }
            for (int i = 2; i * i <= a; i++) {
                if (a % i == 0)
                    return false;
            }
            return true;
        }

        static long bpow(long x, long n, long m) {
            long count = 1;
            if (n == 0) {
                return 1;
            }
            while (n > 0) {
                if ((n & 1) == 1) {
                    count *= x;
                    count %= m;
                }
                x *= x;
                x %= m;
                n >>= 1;
            }
            return count % m;
        }

        static long GCD(long a, long b) {
            if (b == 0) return a;
            return GCD(b, a % b);
        }

        static long lcm(long a, long b) {
            return (a * b) / Library.GCD(a, b);
        }
    }

    class Pair<X, Y> implements Comparable<Pair<X, Y>> {

        public X first;
        public Y second;

        public Pair(X first, Y second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public int hashCode() {
            int hash = 7;
            hash = 11 * hash + Objects.hashCode(this.first);
            hash = 11 * hash + Objects.hashCode(this.second);
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj) {
                return true;
            }
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Pair<?, ?> other = (Pair<?, ?>) obj;
            if (!Objects.equals(this.first, other.first)) {
                return false;
            }
            if (!Objects.equals(this.second, other.second)) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Pair<X, Y> p) {
            return ((Comparable<X>) first).compareTo(p.first);
        }

        @Override
        public String toString() {
            return first + " " + second;
        }
    }

    class Node<E> {
        E element;
        ArrayList<Node<E>> next;

        Node(E element) {
            this.element = element;
            next = new ArrayList<>();
        }
    }

    //    -------------I/O-------------    \\
    private FScanner in;

    private PrintWriter out;

    public static void main(String[] args) {
        new Main().runIO();
    }


    void run() {
        try {
            in = new FScanner(new File("input.txt"));
            out = new PrintWriter(new BufferedWriter(new FileWriter(new File("output.txt"))));
            solve();
            out.close();
            in.close();
        } catch (IOException ex) {
            ex.printStackTrace();
        }
    }

    void runIO() {
        in = new FScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        solve();
        out.close();
        in.close();
    }

    class FScanner {

        private BufferedReader br;
        private StringTokenizer st;

        public FScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException ex) {
                ex.printStackTrace();
            }
        }

        void useString(String s) {
            if (s != null) {
                st = new StringTokenizer(s);
            }
        }

        void updateST() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }

        String next() {
            updateST();
            return st.nextToken();
        }

        Long[] nextLongArray() {
            updateST();
            LinkedList<Long> ll = new LinkedList<>();
            while (st.hasMoreElements()) {
                ll.add(Long.parseLong(st.nextToken()));
            }
            Long[] arr = new Long[1];
            return ll.toArray(arr);
        }

        Integer[] nextIntArray() {
            updateST();
            LinkedList<Integer> ll = new LinkedList<>();
            while (st.hasMoreElements()) {
                ll.add(Integer.parseInt(st.nextToken()));
            }
            Integer[] arr = new Integer[1];
            return ll.toArray(arr);
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            updateST();
            StringBuilder sb = new StringBuilder(st.nextToken());
            while (st.hasMoreElements()) {
                sb.append(st.nextToken());
            }
            return sb.toString();
        }

        void close() {
            try {
                br.close();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
        }

    }
}