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 <bits/stdc++.h>

#define For(i, j, k) for (int i = j; i <= k; i++)
#define Forr(i, j, k) for (int i = j; i >= k; i--)

using namespace std;

const int N = 1010;

int n, m, A, B;
char Map[N][N];

int main() {

	scanf("%d%d%d%d", &n, &m, &A, &B);

	memset(Map, '.', sizeof Map);
	For(i, 1, n) Map[i][m + 1] = '\0';

	if (n & 1) {
		int p = 1;
		while (A && p + 1 <= m) Map[n][p] = '<', Map[n][p + 1] = '>', p += 2, --A;
	}
	if (m & 1) {
		int p = n;
		while (B && p > 1) Map[p - 1][m] = '^', Map[p][m] = 'v', p -= 2, --B;
	}

	Forr(i, n / 2, 1) For(j, 1, m / 2) {
		int x = i * 2 - 1, y = j * 2 - 1;

		if (n % 2 && m % 2 && A == 1 && B == 1 && i == 1 && j == m / 2) {
			Map[x][y] = '^', Map[x + 1][y] = 'v', --B;
			Map[x][y + 1] = '<', Map[x][y + 2] = '>', --A;
		}

		if (A && B < 2) {
			Map[x][y] = '<', Map[x][y + 1] = '>', --A;
			if (A) Map[x + 1][y] = '<', Map[x + 1][y + 1] = '>', --A;
		}
		else if (B) {
			Map[x][y] = '^', Map[x + 1][y] = 'v', --B;
			if (B) Map[x][y + 1] = '^', Map[x + 1][y + 1] = 'v', --B;
		}
	}

	if (A || B) puts("NO");
	else {
		puts("YES");
		For(i, 1, n) puts(Map[i] + 1);
	}

	return 0;
}