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 PYTHON3):

Solution:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**15
mod = 10**9+7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    n,m,a,b = LI()
    if n * m < (a+b) * 2:
        return 'NO'
    r = [['.']*m for _ in range(n)]
    if n % 2 == 1:
        for i in range(min(a,m//2)):
            r[-1][i*2] = '<'
            r[-1][i*2+1] = '>'
            a -= 1

    if m % 2 == 1:
        for i in range(min(b,n//2)):
            r[i*2][-1] = '^'
            r[i*2+1][-1] = 'v'
            b -= 1

    if (a%2) * (b%2) * (n%2) * (m%2) == 1 and n > 2 and m > 2:
        r[-1][-1] = 'v'
        r[-2][-1] = '^'
        r[-3][-1] = '>'
        r[-3][-2] = '<'
        r[-3][-3] = '^'
        r[-2][-3] = 'v'
        a -= 1
        b -= 1

    for i in range(n//2):
        for j in range(m//2):
            if a > 0:
                r[i*2][j*2] = '<'
                r[i*2][j*2+1] = '>'
                if a > 1:
                    r[i*2+1][j*2] = '<'
                    r[i*2+1][j*2+1] = '>'
                a -= 2
            elif b <= 0:
                break
            else:
                r[i*2][j*2] = '^'
                r[i*2+1][j*2] = 'v'
                if b > 1:
                    r[i*2][j*2+1] = '^'
                    r[i*2+1][j*2+1] = 'v'
                b -= 2

    if a > 0 or b > 0:
        return 'NO'

    return 'YES\n' + '\n'.join([''.join(c) for c in r])


print(main())