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>
using namespace std;
int n, m, a, b;
char s[1002][1002];
void init() {
    for (int i = 1; i <= n; i ++) {
        for (int j = 1; j <= m; j ++) {
            s[i][j] = '.';
        }
    }
    if (n%2 == 1) {
        for (int col = 1; a > 0 && col + 1 <= m; col += 2) {
            //printf("ok\n");
            s[n][col] = '<';
            s[n][col+1] = '>';
            a --;
        }

    }
    if (m%2 == 1) {
        for (int row = 1; b > 0 && row + 1 <= n; row += 2) {
            s[row][m] = '^';
            s[row+1][m] = 'v';
            b --;
        }
    }
}
void prt() {
    for (int i = 1; i <= n; i ++) {
        for (int j = 1; j <= m; j ++) {
            printf("%c", s[i][j]);
        }
        printf("\n");
    }
}
void square() {
    for (int i = 1; i+1 <= n; i += 2) {
        for (int j = 1; j+1 <= m; j += 2) {
            if (a >= 2) {
                s[i+0][j+0] = '<'; s[i+0][j+1] = '>';
                s[i+1][j+0] = '<'; s[i+1][j+1] = '>';
                a -= 2;
            } else if (b >= 2) {
                s[i+0][j+0] = '^'; s[i+0][j+1] = '^';
                s[i+1][j+0] = 'v'; s[i+1][j+1] = 'v';
                b -= 2;               
            } else if (a == 1 &&  b == 1 && i+3 > n && j+3 > m && i+2 <= n && j+2 <= m) {
                s[i+0][j+0] = '<', s[i+0][j+1] = '>', s[i+0][j+2] = '^';
                s[i+1][j+0] = '^', s[i+1][j+1] = '.', s[i+1][j+2] = 'v';
                s[i+2][j+0] = 'v', s[i+2][j+1] = '<', s[i+2][j+2] = '>';
                a = b = 0;
            }  else if (a >= 1) {
                s[i+0][j+0] = '<'; s[i+0][j+1] = '>';
                a --;                
            } else if (b >= 1) {
                s[i+0][j+0] = '^'; s[i+1][j+0] = 'v';
                b --;
            } 
        }
    }
    if (a == 0 && b == 0) {
        printf("YES\n");
        prt();
    }  else {
        printf("NO\n");
    }
}
int main() {
    cin >> n >> m >> a >> b;
    init();
    square();
}