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>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pii;
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define sz(a) int(a.size())
const int N=1e3+10;

int gi() {
	int x=0,o=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int n,m,a,b;
char s[N][N];

int main() {
	cin>>n>>m>>a>>b;
	memset(s,'.',sizeof(s));
	if(n&1) {
		for(int i=1;i<m&&a;i+=2) --a,s[n][i]='<',s[n][i+1]='>';
	}
	if(m&1) {
		for(int i=1;i<n&&b;i+=2) --b,s[i][m]='^',s[i+1][m]='v';
	}
	for(int i=1;i<n;i+=2)
		for(int j=1;j<m;j+=2) {
			if(a>=2) {
				a-=2;
				s[i][j]=s[i+1][j]='<';
				s[i][j+1]=s[i+1][j+1]='>';
			}
			else if(b>=2) {
				b-=2;
				s[i][j]=s[i][j+1]='^';
				s[i+1][j]=s[i+1][j+1]='v';
			}
			else if(i==n-2&&j==m-2&&a&&b) {
				--a;--b;
				s[i][j]=s[i+2][j+1]='<';
				s[i][j+1]=s[i+2][j+2]='>';
				s[i][j+2]=s[i+1][j]='^';
				s[i+1][j+2]=s[i+2][j]='v';
			}
			else if(a) {
				--a;
				s[i][j]='<';s[i][j+1]='>';
			}
			else if(b) {
				--b;
				s[i][j]='^';s[i+1][j]='v';
			}
		}
	if(a||b) cout<<"NO";
	else {
		cout<<"YES\n";
		for(int i=1;i<=n;i++,putchar('\n'))
			for(int j=1;j<=m;j++) putchar(s[i][j]);
	}
	return 0;
}