Problem:
Score : 900 points

Problem Statement

Takahashi has an N \times M grid, with N horizontal rows and M vertical columns.
Determine if we can place A 1 \times 2 tiles (1 vertical, 2 horizontal) and B 2 \times 1 tiles (2 vertical, 1 horizontal) satisfying the following conditions, and construct one arrangement of the tiles if it is possible:

All the tiles must be placed on the grid.

Tiles must not stick out of the grid, and no two different tiles may intersect.

Neither the grid nor the tiles may be rotated.

Every tile completely covers exactly two squares.

Constraints

1 \leq N,M \leq 1000

0 \leq A,B \leq 500000

N, M, A and B are integers.

Input

Input is given from Standard Input in the following format:

N M A B

Output

If it is impossible to place all the tiles, print NO.
Otherwise, print the following:

YES
c_{11}...c_{1M}
:
c_{N1}...c_{NM}

Here, c_{ij} must be one of the following characters: ., <, >, ^ and v. Represent an arrangement by using each of these characters as follows:

When c_{ij} is ., it indicates that the square at the i-th row and j-th column is empty;

When c_{ij} is <, it indicates that the square at the i-th row and j-th column is covered by the left half of a 1 \times 2 tile;

When c_{ij} is >, it indicates that the square at the i-th row and j-th column is covered by the right half of a 1 \times 2 tile;

When c_{ij} is ^, it indicates that the square at the i-th row and j-th column is covered by the top half of a 2 \times 1 tile;

When c_{ij} is v, it indicates that the square at the i-th row and j-th column is covered by the bottom half of a 2 \times 1 tile.

Sample Input 1

3 4 4 2

Sample Output 1

YES
<><>
^<>^
v<>v

This is one example of a way to place four 1 \times 2 tiles and three 2 \times 1 tiles on a 3 \times 4 grid.

Sample Input 2

4 5 5 3

Sample Output 2

YES
<>..^
^.<>v
v<>.^
<><>v

Sample Input 3

7 9 20 20

Sample Output 3

NO

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.Random;
public class Main {
	static final long C =  1000000007;
	static final int CY = 1000000000;
	static final int INF = Integer.MAX_VALUE/2;
	StringBuilder sb;
	//セット
	class Set<F,S> {
		F f;
		S s;
		Set(F f, S s) {this.f = f;this.s = s;}
	}
	int[][] G;
	//Map<Integer,List<Integer>> Genb = new HashMap<>();
	int V;
	int E;
	int Venb;
	int Eenb;
	long START_TIME;
	int GenbSize;//Genbグラフの1辺
	Random rand = new Random();
	int[][] DIR = new int[][]{{0,1},{1,0},{-1,0},{0,-1}};

	public void calc() {

		sb = new StringBuilder();


		//入力処理
		IO sc = new IO();

		int n = sc.nextInt() ;
		int m = sc.nextInt();
		int a = sc.nextInt();
		int b = sc.nextInt();

		boolean ans = true;
		char[][] map = new char[n][m];
		for (int i=0; i < n; i++) {
			Arrays.fill(map[i], '.');
		}
		if (n%2 ==1) {
			for (int i=0; i < m-1;i+=2) {
				if (a == 0) break;
				puta(map,0,i);
				a--;
			}
		}
		if (m%2 ==1) {
			for (int i=0; i < n-1;i+=2) {
				if (b==0) break;
				putb(map,i,m-1);
				b--;

			}
		}
		int max = n%2;
		int y =n%2, x=0;
		while(a > 1) {
			if (n-y <=1-max) {
				ans = false;
				//System.err.println(y + "a:" + x);
				break;
			}
			puta(map,y,x);
			puta(map,y+1,x);
			a -= 2;
			x += 2;
			if (m-x <=1) {
				y += 2;
				x = 0;
			}
		}
		while(b > 1) {
			if (n-y <=1-max) {
				ans = false;
				//System.err.println(y + "b:" + x);
				break;
			}
			putb(map,y,x);
			putb(map,y,x+1);
			b -= 2;
			x += 2;
			if (m-x <=1) {
				y += 2;
				x = 0;
			}
		}
		if (n-y <=1-max && a+b > 0) {
			ans = false;

		}else {
			if (n%2 == 1 && m%2 == 1 && a == 1&& b==1&& n-y == 2 && m-x ==3) {

				putb(map,y,x);
				puta(map,y+1,x+1);
				a--;
				b--;
			}else {
				if (a == 1 && !(n-y <=1-max)) {

					puta(map,y,x);
					a -= 1;
					x += 2;
					if (m-x <=1) {
						y += 2;
						x = 0;
					}
				}
				if (b == 1) {
					if (n-y <=1-max) {
						ans = false;

					}else{
						putb(map,y,x);
						b -= 1;
						x += 2;
						if (m-x <=1) {
							y += 2;
							x = 0;
						}
					}
				}
			}
		}



		System.out.println(ans?"YES":"NO");
		if (ans)
		for (int i=0; i < n; i++){
			System.out.println(map[i]);
		}


	}
	void puta(char[][] map ,int y,int x){
		map[y][x] = '<';
		map[y][x+1] = '>';
	}
	void putb(char[][] map ,int y,int x){
		map[y][x] = '^';
		map[y+1][x] = 'v';
	}
	boolean isIn(int y, int x,int h,int w) {
		return 0 <= y && y < h && 0 <= x && x < w;
	}


	public static void main(String[] args) {
		Main main = new Main();
		main.calc();

	}
}
class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public IO() { this(System.in);}
	public IO(InputStream source) { super(System.out); this.in = source;}
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public boolean hasNextLine() { while(hasNextByte() && isNewLine(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] nextIntArray(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] nextLongArray(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] nextDoubleArray(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void nextIntArrays(int[]... a) { for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] nextIntMatrix(int n,int m) { int[][] a = new int[n][]; for(int i=0;i<n;i++) a[i] = nextIntArray(m); return a;}
	public char[][] nextCharMap(int n,int m) { char[][] a = new char[n][]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void close() { super.close(); try {in.close();} catch (IOException e) {}}
}