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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

// author: camypaper
using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using static System.Math;
using static System.Numerics.BigInteger;
using static Program.IO.Scanner;
using Number = System.Int64;

#region IO
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}
	static public class Scanner {
		public static StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
		public static int ri => sc.Integer();
		public static long rl => sc.Long();
		public static string rs => sc.Scan();
		public static double rd => sc.Double();
	}
	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}

}

#endregion

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}
	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = true });
		var solver = new Program.Solver();
		var t = new System.Threading.Thread(solver.Solve, 100000000);
		t.Start();
		t.Join();
		//*/
		//solver.Solve();
		Console.Out.Flush();
	}
}
#endregion

namespace Program {
	public class Solver {
		Random rnd = new Random(0);
		public void Solve() {
			var n = ri;
			var m = ri;
			var w = ri;
			var h = ri;
			if (n == 3 && m == 3 && w == 2 && h == 2) {
				Console.WriteLine("YES");
				Console.WriteLine("^<>");
				Console.WriteLine("v.^");
				Console.WriteLine("<>v");
				return;
			}
			var ans = Enumerate(n, x => new char[m]);
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++) ans[i][j] = '.';
			if (n % 2 == 1) {
				var mi = Min(w, m / 2);
				for (int j = 0; j < mi; j++) {
					ans[n - 1][j * 2] = '<';
					ans[n - 1][j * 2 + 1] = '>';
				}
				w -= mi;
				n--;
			}
			if (m % 2 == 1) {
				var mi = Min(h, n / 2);
				for (int i = 0; i < mi; i++) {
					ans[i * 2][m - 1] = '^';
					ans[i * 2 + 1][m - 1] = 'v';
				}
				h -= mi;
				m--;
			}
			if ((h + w) * 2 > n * m) {
				Console.WriteLine("NO");
				return;
			}
			var rem = new List<int[]>();
			for (int i = 0; i < n; i += 2)
				for (int j = 0; j < m; j += 2) {
					if (h >= 2) {
						ans[i][j] = '^'; ans[i][j + 1] = '^';
						ans[i + 1][j] = 'v'; ans[i + 1][j + 1] = 'v';
						h -= 2;
					}
					else if (w >= 2) {
						ans[i][j] = '<'; ans[i][j + 1] = '>';
						ans[i + 1][j] = '<'; ans[i + 1][j + 1] = '>';
						w -= 2;
					}
					else rem.Add(new int[] { i, j });
				}
			if (h + w <= rem.Count) {
				foreach (var p in rem) {
					var i = p[0]; var j = p[1];
					if (h > 0) {
						h--;
						ans[i][j] = '^';
						ans[i + 1][j] = 'v';
					}
					else if (w > 0) {
						ans[i][j] = '<'; ans[i][j + 1] = '>';
						w--;
					}
				}
			}
			else if (ans[0].Length * ans.Length % 2 == 1 && h + w == 2 && rem.Count == 1) {
				n++; m++;
				ans[n - 3][m - 3] = '^'; ans[n - 3][m - 2] = '<'; ans[n - 3][m - 1] = '>';
				ans[n - 2][m - 3] = 'v'; ans[n - 2][m - 2] = '.'; ans[n - 2][m - 1] = '^';
				ans[n - 1][m - 3] = '<'; ans[n - 1][m - 2] = '>'; ans[n - 1][m - 1] = 'v';
			}
			else {
				Console.WriteLine("NO");
				return;
			}
			Console.WriteLine("YES");
			foreach (var x in ans) Console.WriteLine(x.AsString());
		}

		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n]; for (int i = 0; i < a.Length; ++i) a[i] = f(i); return a;
		}
		static T[][] Enumerate<T>(int n, int m, Func<int, int, T> f) {
			return Enumerate(n, x => Enumerate(m, y => f(x, y)));
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}