Problem: A lot of people in Berland hates rain, but you do not. Rain pacifies, puts your thoughts in order. By these years you have developed a good tradition — when it rains, you go on the street and stay silent for a moment, contemplate all around you, enjoy freshness, think about big deeds you have to do. 

Today everything had changed quietly. You went on the street with a cup contained water, your favorite drink. In a moment when you were drinking a water you noticed that the process became quite long: the cup still contained water because of rain. You decided to make a formal model of what was happening and to find if it was possible to drink all water in that situation. 

Thus, your cup is a cylinder with diameter equals d centimeters. Initial level of water in cup equals h centimeters from the bottom. 

<image>

You drink a water with a speed equals v milliliters per second. But rain goes with such speed that if you do not drink a water from the cup, the level of water increases on e centimeters per second. The process of drinking water from the cup and the addition of rain to the cup goes evenly and continuously. 

Find the time needed to make the cup empty or find that it will never happen. It is guaranteed that if it is possible to drink all water, it will happen not later than after 104 seconds.

Note one milliliter equals to one cubic centimeter.

Input

The only line of the input contains four integer numbers d, h, v, e (1 ≤ d, h, v, e ≤ 104), where:

  * d — the diameter of your cylindrical cup, 
  * h — the initial level of water in the cup, 
  * v — the speed of drinking process from the cup in milliliters per second, 
  * e — the growth of water because of rain if you do not drink from the cup. 

Output

If it is impossible to make the cup empty, print "NO" (without quotes).

Otherwise print "YES" (without quotes) in the first line. In the second line print a real number — time in seconds needed the cup will be empty. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4. It is guaranteed that if the answer exists, it doesn't exceed 104.

Examples

Input

1 2 3 100


Output

NO


Input

1 1 1 1


Output

YES
3.659792366325

Note

In the first example the water fills the cup faster than you can drink from it.

In the second example area of the cup's bottom equals to <image>, thus we can conclude that you decrease the level of water by <image> centimeters per second. At the same time water level increases by 1 centimeter per second due to rain. Thus, cup will be empty in <image> seconds.

Solution (in JAVA):

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

public class Main {

	static int mod = (int) 1e9 + 7;
	static int MAX = (int) 1e9;
	static ArrayList<Integer>[] g;
	static int n, m;
	static long k;
	static int[][] a;
	static int nodes = 0;
	static int edges = 0;
	static boolean[][] done;
	static int[][] ans;
	static int[] dp;

	public static void main(String[] args) {
		FasterScanner s = new FasterScanner();
		PrintWriter out = new PrintWriter(System.out);
		int test = 1;
		testloop: while (test-- > 0) {
			double r = (double) s.nextInt() / 2.0;
			double h = s.nextInt();
			double v = s.nextInt();
			double e = s.nextInt();
			if (Math.PI * r * r * e - v < 0) {
				System.out.println("YES");
				System.out.println(Math.PI * r * r * h / (v - Math.PI * r * r * e));
			} else {
				System.out.println("NO");
			}
		}

		out.close();
	}

	static int dp(int x) {
		int ans = 0;
		int[] pos = new int[n];
		for (int i = 0; i < n; i++) {
			pos[i] = (x & (3 << (2 * i))) >> (2 * i);
		}
		int top[] = new int[4];
		Arrays.fill(top, -1);
		for (int i = n - 1; i >= 0; i--) {
			top[i] = i;
		}

		return ans;
	}

	static class Component implements Comparable<Component> {
		int id;
		int size;

		Component(int id, int size) {
			this.id = id;
			this.size = size;
		}

		@Override
		public int compareTo(Component o) {
			return size - o.size;
		}
	}

	static class Point {
		int x, y;

		Point(int xx, int yy) {
			x = xx;
			y = yy;
		}
	}

	static void dfs(int x, int y, int rem, int val) {
		if (rem <= 0)
			return;
		rem--;
		done[x][y] = true;
		if (check(x + 1, y) && !done[x + 1][y] && a[x + 1][y] >= val)
			dfs(x + 1, y, rem, val);
		if (check(x - 1, y) && !done[x - 1][y] && a[x - 1][y] >= val)
			dfs(x - 1, y, rem, val);
		if (check(x, y + 1) && !done[x][y + 1] && a[x][y + 1] >= val)
			dfs(x, y + 1, rem, val);
		if (check(x, y - 1) && !done[x][y - 1] && a[x][y - 1] >= val)
			dfs(x, y - 1, rem, val);
	}

	static boolean check(int x, int y) {
		return x >= 0 && y >= 0 && x < n && y < m;
	}

	static class Player implements Comparable<Player> {
		String name;
		int score;

		Player(String n, int v) {
			name = n;
			score = v;
		}

		@Override
		public int compareTo(Player o) {
			return o.score - score;
		}
	}

	static class Edge {
		int t, rev, f;
		long cap;

		public Edge(int t, int rev, long cap) {
			this.t = t;
			this.rev = rev;
			this.cap = cap;
		}
	}

	public static List<Edge>[] createGraph(int nodes) {
		List<Edge>[] graph = new List[nodes];
		for (int i = 0; i < nodes; i++)
			graph[i] = new ArrayList<>();
		return graph;
	}

	public static void addEdge(List<Edge>[] graph, int s, int t, long cap) {
		graph[s].add(new Edge(t, graph[t].size(), cap));
		graph[t].add(new Edge(s, graph[s].size() - 1, 0));
	}

	static boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
		Arrays.fill(dist, -1);
		dist[src] = 0;
		int[] Q = new int[graph.length];
		int sizeQ = 0;
		Q[sizeQ++] = src;
		for (int i = 0; i < sizeQ; i++) {
			int u = Q[i];
			for (Edge e : graph[u]) {
				if (dist[e.t] < 0 && e.f < e.cap) {
					dist[e.t] = dist[u] + 1;
					Q[sizeQ++] = e.t;
				}
			}
		}
		return dist[dest] >= 0;
	}

	static long dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, long l) {
		if (u == dest)
			return l;
		for (; ptr[u] < graph[u].size(); ++ptr[u]) {
			Edge e = graph[u].get(ptr[u]);
			if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
				long df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(l, e.cap - e.f));
				if (df > 0) {
					e.f += df;
					graph[e.t].get(e.rev).f -= df;
					return df;
				}
			}
		}
		return 0;
	}

	public static long maxFlow(List<Edge>[] graph, int src, int dest) {
		long flow = 0;
		int[] dist = new int[graph.length];
		while (dinicBfs(graph, src, dest, dist)) {
			int[] ptr = new int[graph.length];
			while (true) {
				long df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
				if (df == 0)
					break;
				flow += df;
			}
		}
		return flow;
	}

	static int ans(ArrayList<Character>[] l, char a, int n) {
		if (n == 1)
			return 1;
		int sum = 0;
		for (int i = 0; i < l[a - 'a'].size(); i++) {
			sum += ans(l, l[a - 'a'].get(i), n - 1);
		}
		return sum;
	}

	static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> order, int u) {
		used[u] = true;
		for (int v : graph[u])
			if (!used[v])
				dfs1(graph, used, order, v);
		order.add(u);
	}

	static void dfs2(List<Integer>[] reverseGraph, int[] comp, int u, int color) {
		comp[u] = color;
		for (int v : reverseGraph[u])
			if (comp[v] == -1)
				dfs2(reverseGraph, comp, v, color);
	}

	public static boolean[] solve2Sat(List<Integer>[] graph) {
		int n = graph.length;
		boolean[] used = new boolean[n];
		List<Integer> order = new ArrayList<>();
		for (int i = 0; i < n; ++i)
			if (!used[i])
				dfs1(graph, used, order, i);

		List<Integer>[] reverseGraph = new List[n];
		for (int i = 0; i < n; i++)
			reverseGraph[i] = new ArrayList<>();
		for (int i = 0; i < n; i++)
			for (int j : graph[i])
				reverseGraph[j].add(i);

		int[] comp = new int[n];
		Arrays.fill(comp, -1);
		for (int i = 0, color = 0; i < n; ++i) {
			int u = order.get(n - i - 1);
			if (comp[u] == -1)
				dfs2(reverseGraph, comp, u, color++);
		}

		for (int i = 0; i < n; ++i)
			if (comp[i] == comp[i ^ 1])
				return null;

		boolean[] res = new boolean[n / 2];
		for (int i = 0; i < n; i += 2)
			res[i / 2] = comp[i] > comp[i ^ 1];
		return res;
	}

	public static int[] createSets(int size) {
		int[] p = new int[size];
		for (int i = 0; i < size; i++)
			p[i] = i;
		return p;
	}

	public static int root(int[] p, int x) {
		return x == p[x] ? x : (p[x] = root(p, p[x]));
	}

	public static void unite(int[] p, int a, int b) {
		a = root(p, a);
		b = root(p, b);
		if (a != b)
			p[a] = b;
	}

	public static boolean nextPermutation(int[] p) {
		for (int a = p.length - 2; a >= 0; --a)
			if (p[a] < p[a + 1])
				for (int b = p.length - 1;; --b)
					if (p[b] > p[a]) {
						int t = p[a];
						p[a] = p[b];
						p[b] = t;
						for (++a, b = p.length - 1; a < b; ++a, --b) {
							t = p[a];
							p[a] = p[b];
							p[b] = t;
						}
						return true;
					}
		return false;
	}

	public static boolean isPrime(long n) {
		if (n <= 1)
			return false;
		for (long i = 2; i * i <= n; i++)
			if (n % i == 0)
				return false;
		return true;
	}

	static class SegTree {
		int[] val;
		int n;

		SegTree(int n) {
			val = new int[2 * n];
			this.n = n;
		}

		void upd(int p, int l) {
			p += n;
			val[p] = l;
			for (; (p >>= 1) != 0;) {
				val[p] = Math.max(val[2 * p], val[2 * p + 1]);

			}
		}

		int query(int l, int r) { // sum on interval [l, r)
			// System.out.println(l+" "+r);
			int res = 0;
			for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
				if ((l & 1) != 0)
					res = Math.max(res, val[l++]);
				if ((r & 1) != 0)
					res = Math.max(res, val[--r]);
			}
			return res;
		}
	}

	static boolean check(int i, int j, int n) {
		if (i >= 0 && j >= 0 && i < n && j < n)
			return true;
		return false;
	}

	public static int[] generateDivisorTable(int n) {
		int[] divisor = new int[n + 1];
		for (int i = 1; i <= n; i++)
			divisor[i] = i;
		for (int i = 2; i * i <= n; i++)
			if (divisor[i] == i)
				for (int j = i * i; j <= n; j += i)
					divisor[j] = i;
		return divisor;
	}

	public static int[][] matrixMul(int[][] a, int[][] b) {
		int n = a.length;
		int m = a[0].length;
		int k = b[0].length;
		int[][] res = new int[n][k];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < k; j++) {
				for (int p = 0; p < m; p++) {
					res[i][j] = (res[i][j] + (int) ((a[i][p] * 1l * b[p][j]) % mod)) % mod;
				}
			}
		}
		return res;
	}

	public static int[][] matrixPow(int[][] a, int p) {
		if (p == 0) {
			return matrixUnit(a.length);
		} else if (p % 2 == 0) {
			return matrixPow(matrixMul(a, a), p / 2);
		} else {
			return matrixMul(a, matrixPow(a, p - 1));
		}
	}

	public static int[][] matrixUnit(int n) {
		int[][] res = new int[n][n];
		for (int i = 0; i < n; ++i) {
			res[i][i] = 1;
		}
		return res;
	}

	static int[] modInv(int n, int mod) {
		int[] ans = new int[n];
		for (int i = 1; i < n; i++)
			ans[i] = (int) pow(i, mod - 2, mod);
		return ans;
	}

	static int[] primes;

	public static long ncr(int n, int r) {
		if (n < r)
			return 0;
		if (n == r)
			return 1;
		if (r == 0)
			return 1;
		if (r < 0)
			return 0;
		long ans = 1;
		for (int i = 0; i < primes.length; i++) {
			long power = count(n, primes[i]) - count(n - r, primes[i]) - count(r, primes[i]);
			ans *= pow(primes[i], power, mod);
			ans %= mod;
		}
		return ans;
	}

	public static long pow(long x, long n, int mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (int) (res * p % mod);
			}
		}
		return res;
	}

	public static long count(int n, int p) {
		long count = 0;
		long z = p;
		while (z <= n) {
			count += n / z;
			z *= p;
		}
		return count;

	}

	public static int[] generatePrimes(int n) {
		boolean[] prime = new boolean[n + 1];
		Arrays.fill(prime, 2, n + 1, true);
		for (int i = 2; i * i <= n; i++)
			if (prime[i])
				for (int j = i * i; j <= n; j += i)
					prime[j] = false;
		int[] primes = new int[n + 1];
		int cnt = 0;
		for (int i = 0; i < prime.length; i++)
			if (prime[i])
				primes[cnt++] = i;

		return Arrays.copyOf(primes, cnt);
	}

	static class Pairxy implements Comparable<Pairxy> {
		int x;
		int y;

		Pairxy(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Pairxy o) {
			return Integer.compare(this.x, o.x);
		}

	}

	static class Pair implements Comparable<Pair> {
		long val;
		int ind;

		Pair(long v, int i) {
			val = v;
			ind = i;
		}

		public int compareTo(Pair o) {
			if (this.val != o.val)
				return Long.compare(this.val, o.val);
			return Integer.compare(this.ind, o.ind);
		}
	}

	public static long C(int n, int r) {
		long ans = 1;
		int x = 1;
		while (x <= r) {
			ans *= n;
			ans /= x;
			x++;
			n--;
		}
		return ans;
	}

	static class DisjointSetsRank {

		int[] p;
		int[] rank;
		int[] size;

		public DisjointSetsRank(int size) {
			p = new int[size];
			this.size = new int[size];
			for (int i = 0; i < size; i++) {
				p[i] = i;
				this.size[i] = 1;
			}
			rank = new int[size];
		}

		public int root(int x) {
			return x == p[x] ? x : (p[x] = root(p[x]));
		}

		public int sameSet(int x, int y) {
			if (root(x) == root(y))
				return 1;
			return 0;

		}

		public int unite(int a, int b) {
			a = root(a);
			b = root(b);
			if (a == b)
				return -1;

			if (rank[a] < rank[b]) {
				p[a] = b;
				size[b] += size[a];
				return a;
			} else {
				p[b] = a;
				size[a] += size[b];
				if (rank[a] == rank[b])
					++rank[a];
				return b;
			}
		}

	}

	static int gcd(long m, long n) {
		long x;
		long y;
		while (m % n != 0) {
			x = n;
			y = m % n;
			m = x;
			n = y;
		}
		return (int) n;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			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 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 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 - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

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

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

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

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