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:
N,M,A,B=map(int,input().split())
Grid=[["."]*M for i in range(N)]
if M%2:
  for i in range(N//2):
    if B>0:
      Grid[2*i][M-1]="^"
      Grid[2*i+1][M-1]="v"
      B-=1
  
if N%2:
  for i in range(M//2):
    if A>0:
      Grid[N-1][2*i]="<"
      Grid[N-1][2*i+1]=">"
      A-=1
  
for i in range((M//2)*(N//2)):
  a,b=i//(M//2),i%(M//2)
  if A>1:
    Grid[2*a][2*b]="<"
    Grid[2*a][2*b+1]=">"
    Grid[2*a+1][2*b]="<"
    Grid[2*a+1][2*b+1]=">"
    A-=2
  elif B>1:
    Grid[2*a][2*b]="^"
    Grid[2*a][2*b+1]="^"
    Grid[2*a+1][2*b]="v"
    Grid[2*a+1][2*b+1]="v"
    B-=2
  else:
    if A==1:
      Grid[2*a][2*b]="<"
      Grid[2*a][2*b+1]=">"
      A-=1
    elif B==1:
      Grid[2*a][2*b]="^"
      Grid[2*a+1][2*b]="v"
      B-=1

if A==B==0:
  print("YES")
  for i in range(N):
    print("".join(Grid[i]))
else:
  if B==1 and M%2:
    if Grid[N-1][M-1]=="." and Grid[N-1][M-2]==">" and Grid[N-2][M-2]==".":
      Grid[N-1][M-2]="<"
      Grid[N-1][M-1]=">"
      Grid[N-1][M-3]="v"
      Grid[N-2][M-3]="^"
      print("YES")
      for i in range(N):
        print("".join(Grid[i]))
    else:
      print("NO")
  else:
    print("NO")