Problem: Monocarp has decided to buy a new TV set and hang it on the wall in his flat. The wall has enough free space so Monocarp can buy a TV set with screen width not greater than a and screen height not greater than b. Monocarp is also used to TV sets with a certain aspect ratio: formally, if the width of the screen is w, and the height of the screen is h, then the following condition should be met: w/h = x/y.

There are many different TV sets in the shop. Monocarp is sure that for any pair of positive integers w and h there is a TV set with screen width w and height h in the shop.

Monocarp isn't ready to choose the exact TV set he is going to buy. Firstly he wants to determine the optimal screen resolution. He has decided to try all possible variants of screen size. But he must count the number of pairs of positive integers w and h, beforehand, such that (w ≤ a), (h ≤ b) and (w/h = x/y).

In other words, Monocarp wants to determine the number of TV sets having aspect ratio x/y, screen width not exceeding a, and screen height not exceeding b. Two TV sets are considered different if they have different screen width or different screen height.

Input

The first line contains four integers a, b, x, y (1 ≤ a, b, x, y ≤ 10^{18}) — the constraints on the screen width and height, and on the aspect ratio.

Output

Print one integer — the number of different variants to choose TV screen width and screen height so that they meet the aforementioned constraints.

Examples

Input

17 15 5 3


Output

3


Input

14 16 7 22


Output

0


Input

4 2 6 4


Output

1


Input

1000000000000000000 1000000000000000000 999999866000004473 999999822000007597


Output

1000000063

Note

In the first example, there are 3 possible variants: (5, 3), (10, 6), (15, 9).

In the second example, there is no TV set meeting the constraints.

In the third example, there is only one variant: (3, 2).

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class TaskB
{
	public static void main(String[] args)
	{
		new TaskB(System.in, System.out);
	}

	static class Solver implements Runnable
	{
		long a, b, x, y;
//		BufferedReader in;
		InputReader in;
		PrintWriter out;

		void solve() throws IOException
		{
			a = in.nextLong();
			b = in.nextLong();
			x = in.nextLong();
			y = in.nextLong();

			long gcd = CMath.gcd(x, y);

			x /= gcd;
			y /= gcd;

			long min = Math.min(a / x, b / y);

			out.println(min);
		}

		void debug(Object... o)
		{
			System.err.println(Arrays.deepToString(o));
		}

//		uncomment below line to change to BufferedReader
//		public Solver(BufferedReader in, PrintWriter out)
		public Solver(InputReader in, PrintWriter out)
		{
			this.in = in;
			this.out = out;
		}

		@Override
		public void run()
		{
			try
			{
				solve();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}
		}

	}

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

		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 nextInt()
		{
			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 & 15;

				c = read();
			} while (!isSpaceChar(c));

			return res * sgn;
		}

		public int[] nextIntArray(int arraySize)
		{
			int array[] = new int[arraySize];

			for (int i = 0; i < arraySize; i++)
				array[i] = nextInt();

			return array;
		}

		public long nextLong()
		{
			int c = read();

			while (isSpaceChar(c))
				c = read();

			int sign = 1;

			if (c == '-')
			{
				sign = -1;

				c = read();
			}

			long result = 0;

			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();

				result *= 10;
				result += c & 15;

				c = read();
			} while (!isSpaceChar(c));

			return result * sign;
		}

		public long[] nextLongArray(int arraySize)
		{
			long array[] = new long[arraySize];

			for (int i = 0; i < arraySize; i++)
				array[i] = nextLong();

			return array;
		}

		public float nextFloat()
		{
			float result, div;
			byte c;

			result = 0;
			div = 1;
			c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean isNegative = (c == '-');

			if (isNegative)
				c = (byte) read();

			do
			{
				result = result * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					result += (c - '0') / (div *= 10);

			if (isNegative)
				return -result;

			return result;
		}

		public double nextDouble()
		{
			double ret = 0, div = 1;
			byte c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean neg = (c == '-');

			if (neg)
				c = (byte) read();

			do
			{
				ret = ret * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);

			if (neg)
				return -ret;

			return ret;
		}

		public String next()
		{
			int c = read();

			while (isSpaceChar(c))
				c = read();

			StringBuilder res = new StringBuilder();

			do
			{
				res.appendCodePoint(c);

				c = read();
			} while (!isSpaceChar(c));

			return res.toString();
		}

		public String nextLine()
		{
			int c = read();

			StringBuilder result = new StringBuilder();

			do
			{
				result.appendCodePoint(c);

				c = read();
			} while (!isNewLine(c));

			return result.toString();
		}

		public boolean isNewLine(int c)
		{
			return c == '\n';
		}

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

		public void close()
		{
			try
			{
				stream.close();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}
		}

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

	}

	static class CMath
	{
		static long power(long number, long power)
		{
			if (number == 1 || number == 0 || power == 0)
				return 1;

			if (power == 1)
				return number;

			if (power % 2 == 0)
				return power(number * number, power / 2);
			else
				return power(number * number, power / 2) * number;
		}

		static long modPower(long number, long power, long mod)
		{
			if (number == 1 || number == 0 || power == 0)
				return 1;

			number = mod(number, mod);

			if (power == 1)
				return number;

			long square = mod(number * number, mod);

			if (power % 2 == 0)
				return modPower(square, power / 2, mod);
			else
				return mod(modPower(square, power / 2, mod) * number, mod);
		}

		static long moduloInverse(long number, long mod)
		{
			return modPower(number, mod - 2, mod);
		}

		static long mod(long number, long mod)
		{
			return number - (number / mod) * mod;
		}

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

		static long min(long... arr)
		{
			long min = arr[0];

			for (int i = 1; i < arr.length; i++)
				min = Math.min(min, arr[i]);

			return min;
		}

		static long max(long... arr)
		{
			long max = arr[0];

			for (int i = 1; i < arr.length; i++)
				max = Math.max(max, arr[i]);

			return max;
		}

		static int min(int... arr)
		{
			int min = arr[0];

			for (int i = 1; i < arr.length; i++)
				min = Math.min(min, arr[i]);

			return min;
		}

		static int max(int... arr)
		{
			int max = arr[0];

			for (int i = 1; i < arr.length; i++)
				max = Math.max(max, arr[i]);

			return max;
		}

	}

	static class Utils
	{
		static boolean nextPermutation(int[] arr)
		{
			for (int a = arr.length - 2; a >= 0; --a)
			{
				if (arr[a] < arr[a + 1])
				{
					for (int b = arr.length - 1; ; --b)
					{
						if (arr[b] > arr[a])
						{
							int t = arr[a];

							arr[a] = arr[b];
							arr[b] = t;

							for (++a, b = arr.length - 1; a < b; ++a, --b)
							{
								t = arr[a];
								arr[a] = arr[b];
								arr[b] = t;
							}

							return true;
						}
					}
				}
			}

			return false;
		}

	}

	public TaskB(InputStream inputStream, OutputStream outputStream)
	{
//		uncomment below line to change to BufferedReader
//		BufferedReader in = new BufferedReader(new InputStreamReader(inputStream));
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Thread thread = new Thread(null, new Solver(in, out), "TaskB", 1 << 29);

		try
		{
			thread.start();
			thread.join();
		}
		catch (InterruptedException e)
		{
			e.printStackTrace();
		}
		finally
		{
			in.close();
			out.flush();
			out.close();
		}
	}

}