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 L long long
using namespace std;
int n,m,a,b,c,d;
char s[1010][1010];
inline void orz1(int i,int j)
{
    if(a)
      {
       a--;
       s[i][j]='<';
       s[i][j+1]='>';
      }
}
inline void orz2(int i,int j)
{
    if(b)
      {
       b--;
       s[i][j]='^';
       s[i+1][j]='v';
      }
}
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j;
	scanf("%d%d%d%d",&n,&m,&a,&b);
	for(i=1;i<=n;i++)
	  for(j=1;j<=m;j++)
	    s[i][j]='.';
	if(n&1)
	  for(i=1;i<m;i+=2)
	    orz1(n,i);
	if(m&1)
	  for(i=1;i<n;i+=2)
	    orz2(i,m);
	for(i=1;i<n;i+=2)
	  for(j=1;j<m;j+=2)
	    if(a>=2 || a==1 && (!b || b==1 && !(i==n-2 && j==m-2)))
	      {
           orz1(i,j);
           orz1(i+1,j);
          }
        else if(b>=2 || b==1 && (!a || a==1 && !(i==n-2 && j==m-2)))
          {
           orz2(i,j);
           orz2(i,j+1);
          }
        else if(a==1 && b==1 && i==n-2 && j==m-2)
          {
           a++;
           b++;
           orz1(i,j);
           orz1(i+2,j+1);
           orz2(i+1,j);
           orz2(i,j+2);
          }
    if(!a && !b)
      {
       printf("YES\n");
       for(i=1;i<=n;i++)
         printf("%s\n",s[i]+1);
      }
    else
      printf("NO\n");
	return 0;
}