Problem: 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.

Examples

Input

3 4 4 2


Output

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


Input

4 5 5 3


Output

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


Input

7 9 20 20


Output

NO

Solution (in CPP):

Solution:
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>

using namespace std;

int main(){
	ios_base::sync_with_stdio(false);
	int n, m, a, b;
	cin >> n >> m >> a >> b;
	vector<string> field(n, string(m, '.'));
	if(n % 2 == 1){
		for(int i = 0; a > 0 && i + 1 < m; i += 2){
			field[n - 1][i]     = '<';
			field[n - 1][i + 1] = '>';
			--a;
		}
	}
	if(m % 2 == 1){
		for(int i = 0; b > 0 && i + 1 < n; i += 2){
			field[i][m - 1]     = '^';
			field[i + 1][m - 1] = 'v';
			--b;
		}
	}
	for(int i = 0; i + 1 < n; i += 2){
		for(int j = 0; j + 1 < m; j += 2){
			if(a >= 2){
				field[i + 0][j + 0] = '<';
				field[i + 0][j + 1] = '>';
				field[i + 1][j + 0] = '<';
				field[i + 1][j + 1] = '>';
				a -= 2;
			}else if(b >= 2){
				field[i + 0][j + 0] = '^';
				field[i + 0][j + 1] = '^';
				field[i + 1][j + 0] = 'v';
				field[i + 1][j + 1] = 'v';
				b -= 2;
			}else if(a > 0){
				field[i + 0][j + 0] = '<';
				field[i + 0][j + 1] = '>';
				a -= 1;
			}else if(b > 0){
				field[i + 0][j + 0] = '^';
				field[i + 1][j + 0] = 'v';
				b -= 1;
			}
		}
	}
	if(n >= 3 && m >= 3 &&
	   n % 2 == 1 && m % 2 == 1 &&
	   b == 1 &&
	   field[n - 3][m - 3] == '<' &&
	   field[n - 3][m - 1] == '^' &&
	   field[n - 2][m - 3] == '.' &&
	   field[n - 1][m - 3] == '<')
	{
		field[n - 3][m - 3] = '<';
		field[n - 3][m - 2] = '>';
		field[n - 3][m - 1] = '^';
		field[n - 2][m - 1] = 'v';
		field[n - 2][m - 3] = '^';
		field[n - 1][m - 3] = 'v';
		field[n - 1][m - 2] = '<';
		field[n - 1][m - 1] = '>';
		--b;
	}
	if(a > 0 || b > 0){
		cout << "NO" << endl;
	}else{
		cout << "YES" << endl;
		for(const auto& line : field){ cout << line << endl; }
	}
	return 0;
}