The main street of Berland is a straight line with n houses built along it (n is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to n - 1 in the order from the beginning of the street to the end (in the picture: from left to right). The houses with even numbers are at the other side of the street and are numbered from 2 to n in the order from the end of the street to its beginning (in the picture: from right to left). The corresponding houses with even and odd numbers are strictly opposite each other, that is, house 1 is opposite house n, house 3 is opposite house n - 2, house 5 is opposite house n - 4 and so on.

<image>

Vasya needs to get to house number a as quickly as possible. He starts driving from the beginning of the street and drives his car to house a. To get from the beginning of the street to houses number 1 and n, he spends exactly 1 second. He also spends exactly one second to drive the distance between two neighbouring houses. Vasya can park at any side of the road, so the distance between the beginning of the street at the houses that stand opposite one another should be considered the same.

Your task is: find the minimum time Vasya needs to reach house a.

Input

The first line of the input contains two integers, n and a (1 ≤ a ≤ n ≤ 100 000) — the number of houses on the street and the number of the house that Vasya needs to reach, correspondingly. It is guaranteed that number n is even.

Output

Print a single integer — the minimum time Vasya needs to get from the beginning of the street to house a.

Examples

Input

4 2


Output

2


Input

8 5


Output

3

Note

In the first sample there are only four houses on the street, two houses at each side. House 2 will be the last at Vasya's right.

The second sample corresponds to picture with n = 8. House 5 is the one before last at Vasya's left.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Iterator;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class KSN {

	static PrintWriter out = new PrintWriter(System.out);

	static void input() throws IOException {
		Reader.init(System.in);
		Reader.delimiter = " ";
	}

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub

		input();
		solve();
	}

	static void solve() throws IOException {

		int n = Reader.nextInt();
		int a = Reader.nextInt();

		int ans = 1;

		if (a % 2 != 0)
			ans += (a - 1) / 2;

		else
			ans += (n - a) / 2;

		out.println(ans);
		out.flush();
		out.close();

	}

	static class Reader {

		static BufferedReader reader;
		static StringTokenizer tokenizer;
		static String delimiter = " ";

		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer(" ");
		}

		static String next() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {

				tokenizer = new StringTokenizer(reader.readLine());
			}
			return tokenizer.nextToken(delimiter);
		}

		static String nextLine() throws IOException {
			return reader.readLine();
		}

		static char nextChar() throws IOException {
			return (char) reader.read();
		}

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

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

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

		static long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}

			return arr;
		}

		static int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

	}

}