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 debug(x) cerr<<#x<<'='<<x<<endl
#define set0(x) memset(x,0,sizeof(x))
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pii;
template<typename T> void read(T &x){
	x = 0;char ch = getchar();ll f = 1;
	while(!isdigit(ch)){if(ch == '-')f*=-1;ch=getchar();}
	while(isdigit(ch)){x = x*10+ch-48;ch=getchar();}x*=f;
}

int n,m,a,b,cn,cm,fpn,fpm;
char ans[1010][1010];

void allocate(){
	if(fpn == 0){
		cout<<"NO\n";
		exit(0);
	}
	cn = (n/2+1-fpn)*2-2;
	cm = fpm*2-2;
	fpm-=1;
	if(fpm == 0)fpm = m/2,fpn-=1;
}

int main() {
	read(n);read(m);read(a);read(b);
	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			ans[i][j] = '.';
		}
	}
	if(m%2 == 1){
		int p = 0;
		while(b && p+1<n){
			ans[p][m-1] = '^';
			ans[p+1][m-1] = 'v';
			p+=2;
			b-=1;
		}
	}
	if(n%2 == 1){
		int p = m-1;
		while(a && p-1>=0){
			ans[n-1][p] = '>';
			ans[n-1][p-1] = '<';
			p-=2;
			a-=1;
		}
	}
	fpn = n/2;
	fpm = m/2;
	while(a>1){
		allocate();
		ans[cn][cm] = '<';
		ans[cn][cm+1] = '>';
		ans[cn+1][cm] = '<';
		ans[cn+1][cm+1] = '>';
		a-=2;
	}
	while(b>1){
		allocate();
		ans[cn][cm] = '^';
		ans[cn+1][cm] = 'v';
		ans[cn][cm+1] = '^';
		ans[cn+1][cm+1] = 'v';
		b-=2;
	}
	if(a>0 && b>0 && n%2 == 1 && m%2 == 1){
		allocate();
		ans[n-1][0] = 'v';
		ans[n-2][0] = '^';
		ans[n-3][0] = '<';
		ans[n-3][1] = '>';
	}else{
		if(a>0){
			allocate();
			ans[cn][cm] = '<';
			ans[cn][cm+1] = '>';
		}
		if(b>0){
			allocate();
			ans[cn][cm] = '^';
			ans[cn+1][cm] = 'v';
		}
	}
	cout<<"YES\n";
	for(int i=0;i<n;i++){
		cout<<ans[i]<<endl;
	}
	return 0;
}