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.*;
import java.util.*;


public class Main_Round460Div2_E {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int a = sc.nextInt();
		int b = sc.nextInt();
		long p = sc.nextInt();
		long x = sc.nextLong();

		b %= p;
		long ans = 0;

		if (b == 0) {
			ans = x / p;
		} else {
			for (int n = 1; n < p; n++) {
				long aa = modPow(a, n, (int)p);

				long[] xy = new long[2];
				@SuppressWarnings("unused")
				long gcd = extgcd(aa, (long)p, xy);

				long xx = (xy[0] * b % p + p) % p;
				if (xx > n) {
					long tmp = n + (n + p - xx) * (p - 1);
					if (tmp <= x) {
//						pr.printf("%d %d\n", n, tmp);
						ans += 1;
						ans += (x - tmp) / (p * (p - 1));
					}
				} else if (xx < n) {
					long tmp = n + (n - xx) * (p - 1);
					if (tmp <= x) {
//						pr.printf("%d %d\n", n, tmp);
						ans += 1;
						ans += (x - tmp) / (p * (p - 1));
					}
				} else {
					long tmp = n;
					if (tmp <= x) {
//						pr.printf("%d %d\n", n, tmp);
						ans += 1;
						ans += (x - tmp) / (p * (p - 1));
					}
				}
			}
		}

		pr.println(ans);
	}

	private static long extgcd(long n, long m, long[] xy) {
		if (m == 0) {
			xy[0] = 1;
			xy[1] = 0;

			return n;
		} else {
			long ret = extgcd(m, n % m, xy);

			long tmp = xy[1];
			xy[1] = xy[0] - n / m * tmp;
			xy[0] = tmp;

			return ret;
		}
	}

	private static long modPow(long a, long n, int MOD) {
		long loop = n;
		long ret = 1;
		long x = a;
		while (loop > 0) {
			if (loop % 2 == 1) {
				ret = ret * x % MOD;
			}
			x = x * x % MOD;
			loop /= 2;
		}

		return ret;
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);

		solve();

		pr.close();
		sc.close();
	}

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

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

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}