Problem: Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b   (mod\;p), where a, b, p$$$ are all known constants.

Input

The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b < p, 1 ≤ x ≤ 10^{12}). It is guaranteed that p is a prime.

Output

Print a single integer: the number of possible answers n.

Examples

Input

2 3 5 8


Output

2


Input

4 6 7 13


Output

1


Input

233 233 10007 1


Output

1

Note

In the first sample, we can see that n=2 and n=8 are possible answers.

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.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
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);
        ECongruenceEquation solver = new ECongruenceEquation();
        solver.solve(1, in, out);
        out.close();
    }

    static class ECongruenceEquation {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            long a = in.nextLong();
            long b = in.nextLong();
            long p = in.nextLong();
            long x = in.nextLong();

//        long lpm = (x / p) * p;
//        long t = x / p;
//
//        long[] ap = new long[(int) p];
//
//        ap[0] = 1;
//
//        for (int i = 1; i < p; i++) {
//            ap[i] = ap[i - 1] * a;
//            ap[i] %= p;
//        }
//
//        long[] miap = new long[(int) p];
//
//        Arrays.fill(miap, -1);
//
//        for (int i = 0; i < p; i++) {
//            if (miap[(int) ap[i]] == -1) {
//                miap[(int) ap[i]] = i;
//            }
//        }

            long maxi = x / (p - 1);

            long xx = maxi * (p - 1);

            long ans = 0;
            for (int r = 0; r < p - 1; r++) {
                long val = b;
                long ap = pow(a, r, p);
                long api = pow(ap, p - 2, p);
                val *= api;
                val %= p;

                long st = r - val;
                if (st < 0) {
                    st += p;
                }

                long cmaxi = maxi;

                if (xx + r > x) {
                    cmaxi--;
                }

                if (st > cmaxi)
                    continue;

                long rem = cmaxi - st;

                ans += (rem / p) + 1;
            }

            out.println(ans);
        }

        long pow(long a, long p, long mod) {
            if (p == 0) {
                return 1;
            }

            long t = pow(a, p / 2, mod);

            if (p % 2 != 0) {
                return (((t * t) % mod) * a) % mod;
            } else {
                return (t * t) % mod;
            }
        }

    }

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

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

        }

    }
}