Submission #187988

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Source Code Expand

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

import static java.util.Arrays.*;

public class Main {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int n = io.nextInt();
			int d = io.nextInt();
			int txx = io.nextInt();
			int tyy = io.nextInt();
			
			if(txx % d != 0 || tyy % d != 0) {
				io.out.println(0);
				return;
			}

			int tx = Math.abs(txx / d);
			int ty = Math.abs(tyy / d);
			
			double[][] comb = new double[1001][1001];
			for(int i = 0; i < comb.length; i++) {
				comb[i][0] = comb[i][i] = 1;
				for(int j = 1; j < i; j++) {
					comb[i][j] = comb[i-1][j-1] + comb[i-1][j];
				}
			}
			
			double ans = 0;
			for(int i = 0; i <= n; i++) {
				if(i < tx || n - i < ty) continue;
				if(tx % 2 != i % 2 || (n - i) % 2 != ty % 2) {
					continue;
				}

				int xr = (i + tx) / 2;
				int yr = (n - i + ty) / 2;
				double vx = comb[i][xr] * pow(0.5, i);
				double vy = comb[n-i][yr] * pow(0.5, n - i);
				ans += comb[n][i] * pow(0.5, n) * vx * vy;
			}
			io.out.printf("%.15f\n", ans);
		}
	}
	static double pow(double n, int r) {
		double res = 1;
		for(; r != 0; r >>>= 1, n = n * n) {
			if((r&1) == 1) {
				res = res * n;
			}
		}
		return res;
	}


	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) {
		T t = x[i];
		x[i] = x[j];
		x[j] = t;
	}
	
	static void swap(int[] x, int i, int j) {
		int t = x[i];
		x[i] = x[j];
		x[j] = t;
	}
	

	static void radixSort(int[] xs) {
		int[] cnt = new int[(1<<16)+1];
		int[] ys = new int[xs.length];
		
		for(int j = 0; j <= 16; j += 16) {
			Arrays.fill(cnt, 0);
			for(int x : xs) { cnt[(x>>j&0xFFFF)+1]++; }
			for(int i = 1; i < cnt.length; i++) { cnt[i] += cnt[i-1]; }
			for(int x : xs) { ys[cnt[x>>j&0xFFFF]++] = x; }
			{ final int[] t = xs; xs = ys; ys = t; }
		}
	}
	
	static void radixSort(long[] xs) {
		int[] cnt = new int[(1<<16)+1];
		long[] ys = new long[xs.length];
		
		for(int j = 0; j <= 48; j += 16) {
			Arrays.fill(cnt, 0);
			for(long x : xs) { cnt[(int)(x>>j&0xFFFF)+1]++; }
			for(int i = 1; i < cnt.length; i++) { cnt[i] += cnt[i-1]; }
			for(long x : xs) { ys[cnt[(int)(x>>j&0xFFFF)]++] = x; }
			{ final long[] t = xs; xs = ys; ys = t; }
		}
	}
	

	static void arrayIntSort(int[][] x, int... keys) {
		Arrays.sort(x, new ArrayIntsComparator(keys));
	}
	
	static class ArrayIntsComparator implements Comparator<int[]> {
		final int[] KEY;
		
		public ArrayIntsComparator(int... key) {
			KEY = key;
		}
		
		@Override
		public int compare(int[] o1, int[] o2) {
			for(int k : KEY) if(o1[k] != o2[k]) return o1[k] - o2[k];
			return 0;
		}
	}
	
	static class ArrayIntComparator implements Comparator<int[]> {
		final int KEY;
		
		public ArrayIntComparator(int key) {
			KEY = key;
		}
		
		@Override
		public int compare(int[] o1, int[] o2) {
			return o1[KEY] - o2[KEY];
		}
	}
	
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try {
			run();
		}
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}

	public static void main(String[] args) throws IOException {
		new Main().main();
	}
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIO(String ins, String outs) throws IOException {
			out.flush();
			out.close();
			in.close();
			in = new BufferedReader(new FileReader(ins));
			out = new PrintWriter(new FileWriter(outs));
			System.err.println("reading from " + ins);
		}

		//		private static final int BUFFER_SIZE = 50 * 200000;
		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; }
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public int read() throws IOException {
			if(pos >= readLen) {
				pos = 0;
				readLen = in.read(buffer);
				if(readLen <= 0) { throw new EndOfFileRuntimeException(); }
			}
			return buffer[pos++];
		}

		public int nextInt() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			
			int i = 0;
			int ret = 0;
			if(str[0] == '-') { i = 1; }
			for(; i < len; i++) ret = ret * 10 + str[i] - '0';
			if(str[0] == '-') { ret = -ret; }
			return ret;
//			return Integer.parseInt(nextString());
		}

		public long nextLong() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			
			int i = 0;
			long ret = 0;
			if(str[0] == '-') { i = 1; }
			for(; i < len; i++) ret = ret * 10 + str[i] - '0';
			if(str[0] == '-') { ret = -ret; }
			return ret;
//			return Long.parseLong(nextString());
		}

		public char nextChar() throws IOException {
			while(true) {
				final int c = read();
				if(!isSpace[c]) { return (char)c; }
			}
		}
		
		int reads(int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					
					if(str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					
					str[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}
		
		int reads(char[] cs, int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					cs[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}

		public char[] nextLine() throws IOException {
			int len = 0;
			str[len++] = nextChar();
//			str[len++] = (char)read();
			len = reads(len, isLineSep);
			
			try {
				if(str[len-1] == '\r') { len--; read(); }
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return Arrays.copyOf(str, len);
		}

		public String nextString() throws IOException {
			return new String(next());
		}

		public char[] next() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public int next(char[] cs) throws IOException {
			int len = 0;
			cs[len++] = nextChar();
			len = reads(cs, len, isSpace);
			return len;
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(nextString());
		}

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

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

		public int[][] nextIntArray2D(final int n, final int k) throws IOException {
			final int[][] res = new int[n][];
			for(int i = 0; i < n; i++) {
				res[i] = nextIntArray(k);
			}
			return res;
		}

		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException {
			final int[][] res = new int[n][k+1];
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < k; j++) {
					res[i][j] = nextInt();
				}
				res[i][k] = i;
			}
			return res;
		}

		public double[] nextDoubleArray(final int n) throws IOException {
			final double[] res = new double[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

	}

}

Submission Info

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