Problem: While sailing on a boat, Inessa noticed a beautiful water lily flower above the lake's surface. She came closer and it turned out that the lily was exactly H centimeters above the water surface. Inessa grabbed the flower and sailed the distance of L centimeters. Exactly at this point the flower touched the water surface.

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Suppose that the lily grows at some point A on the lake bottom, and its stem is always a straight segment with one endpoint at point A. Also suppose that initially the flower was exactly above the point A, i.e. its stem was vertical. Can you determine the depth of the lake at point A?

Input

The only line contains two integers H and L (1 ≤ H < L ≤ 10^{6}).

Output

Print a single number — the depth of the lake at point A. The absolute or relative error should not exceed 10^{-6}.

Formally, let your answer be A, and the jury's answer be B. Your answer is accepted if and only if \frac{|A - B|}{max{(1, |B|)}} ≤ 10^{-6}.

Examples

Input


1 2


Output


1.5000000000000


Input


3 5


Output


2.6666666666667

Solution (in JAVA):

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

public class WaterLily {

	public static void main(String[] args) throws Exception {
		Reader file = new Reader();

		double h = file.nextDouble();
		double l = file.nextDouble();

		double tmp = Math.pow(l, 2) - Math.pow(h, 2);

		System.out.println(tmp / (2 * h));
	}

	static class Reader {
		private final int BUFFER_SIZE = 1 << 16;
		private char nullChar = (char) 0;
		private byte[] buf = new byte[BUFFER_SIZE];
		private int bufferPointer, bytesRead;
		private char c = nullChar;
		private BufferedInputStream in;
		private char delimeter = ' ';

		public void close() throws IOException {
			in.close();
		}

		public Reader() {
			in = new BufferedInputStream(System.in, BUFFER_SIZE);
			bufferPointer = bytesRead = 0;
		}

		public Reader(InputStream read) {
			in = new BufferedInputStream(read, BUFFER_SIZE);
			bufferPointer = bytesRead = 0;
		}

		public Reader(String s) throws FileNotFoundException {
			try {
				in = new BufferedInputStream(new FileInputStream(new File(s)), BUFFER_SIZE);
			} catch (FileNotFoundException e) {
				throw new FileNotFoundException();
			}
			bufferPointer = bytesRead = 0;
		}

		private char nextChar() {
			while (bufferPointer == bytesRead) {
				try {
					bytesRead = in.read(buf);
				} catch (Exception e) {
					return nullChar;
				}
				if (bytesRead == -1) {
					return nullChar;
				}
				bufferPointer = 0;
			}
			try {
				return (char) buf[bufferPointer++];
			} catch (ArrayIndexOutOfBoundsException e) {
				throw new NoSuchElementException("No Line Found");
			}
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while (c < 32 || c == delimeter)
				c = nextChar();
			while (c != nullChar) {
				if (c == '\n' || c == '\r' || c == delimeter) {
					break;
				}
				res.append(c);
				c = nextChar();
			}
			if (c == '\n')
				c = nextChar();
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while (c == delimeter) {
				c = nextChar();
			}
			while (c != nullChar) {
				if (c == '\n' || c == '\r') {
					c = nextChar();
					break;
				}
				res.append(c);
				c = nextChar();
			}
			if (c == '\n')
				c = nextChar();
			return res.toString();
		}

		/**
		 * Note: Setting the delimeter to "-" will remove the methods ability to read
		 * negatives.
		 */
		public int nextInt() {
			return (int) nextLong();
		}

		/**
		 * Note: Setting the delimeter to "-" will remove the methods ability to read
		 * negatives.
		 */
		public long nextLong() {
			while (c == delimeter || c < 32)
				c = nextChar();
			if (c < '0' && c != '-' || c > '9')
				throw new InputMismatchException("" + c);
			boolean neg = (c == '-');
			if (neg)
				c = nextChar();
			long res = 0;
			do {
				res = (res << 3) + (res << 1) + c - '0';
			} while ((c = nextChar()) >= '0' && c <= '9');
			return neg ? -res : res;
		}

		/**
		 * Note: Setting the delimeter to "-" or "." may remove the methods ability to
		 * read negatives or decimals.
		 */
		public double nextDouble() {
			while (c == delimeter || c < 32)
				c = nextChar();
			if (c < '0' && c != '-' && c != '.' || c > '9')
				throw new InputMismatchException("" + c);
			boolean neg = (c == '-');
			if (neg)
				c = nextChar();
			double res = 0.0;
			while (c >= '0' && c <= '9') {
				res = res * 10 + c - '0';
				c = nextChar();
			}
			if (c == '.') {
				double div = 1;
				while ((c = nextChar()) >= '0' && c <= '9') {
					res += (c - '0') / (div *= 10);
				}
			}
			return neg ? -res : res;
		}

		public BigInteger nextBigInteger() {
			while (c == delimeter || c < 32)
				c = nextChar();
			if (!Character.isDigit(c) && c != '-') {
				throw new InputMismatchException();
			}
			StringBuilder strNum = new StringBuilder();
			if (c == '-') {
				strNum.append("-");
				c = nextChar();
			}
			while (Character.isDigit(c)) {
				strNum.append(c);
				c = nextChar();
			}
			return new BigInteger(strNum.toString());
		}

		public BigDecimal nextBigDecimal() {
			while (c == delimeter || c < 32)
				c = nextChar();
			if (!Character.isDigit((c)) && c != '-' && c != '.')
				throw new InputMismatchException();
			StringBuilder strNum = new StringBuilder();
			if (c == '-') {
				strNum.append("-");
				c = nextChar();
			}
			while (Character.isDigit(c) || c == '.') {
				strNum.append(c);
				c = nextChar();
			}
			return new BigDecimal(strNum.toString());
		}

		public char delimeter() {
			return delimeter;
		}

		public void useDelimeter(char c) {
			delimeter = c;
		}

		public boolean hasNext() throws IOException {
			if (c >= 32)
				return true;
			in.mark(BUFFER_SIZE);
			char save = c;
			int savePointer = bufferPointer;
			while (true) {
				c = nextChar();
				if (bytesRead == -1 || c == nullChar)
					return false;
				if (c >= 32) {
					return true;
				}
				if (c == '\n' || c == '\r') {
					for (int i = 0; i < 2; i++) {
						c = nextChar();
						if (c >= 5) {
							in.reset();
							c = save;
							bufferPointer = savePointer;
							return true;
						}
						if (bytesRead == -1 || c == nullChar)
							return false;
					}
				}
			}
		}
	}
}