//
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<ll, P>IP;
typedef vector<ll> V;
typedef vector<V> V2;
typedef vector<vector<P> > G;
void g_dir(G &graph, ll a, ll b, ll w = 1){graph[a].push_back(P(b, w));}
void g_undir(G &graph, ll a, ll b, ll w = 1){g_dir(graph, a, b, w);g_dir(graph, b, a, w);}
#define rep(i, n) for(ll (i) = 0; (i) < (n); (i)++)
#define rep1(i, n) for(ll (i) = 1; (i) <= (n); (i)++)
#define rrep(i, n) for(ll (i) = (n) - 1; (i) >= 0; (i)--)
#define rrep1(i, n) for(ll (i) = (n); (i) >= 1; (i)--)
template<class T> void chmax(T &a, const T &b){if(a < b){a = b;}}
template<class T> void chmin(T &a, const T &b){if(a > b){a = b;}}
const ll INF = 1145141919;
const ll MOD = 1000000007;
const ll NUM = 101010;

char mp[1010][1010];

int main(){

    ll H, W, w, h;
    cin >> H >> W >> w >> h;
    rep1(y, H)rep1(x, W)mp[y][x] = '.';
    for(ll y = 1; W % 2 && y + 1 <= H && h; y += 2){
        mp[y][W] = '^';
        mp[y + 1][W] = 'v';
        h--;
    }
    for(ll x = 1; H % 2 && x + 1 <= W && w; x += 2){
        mp[H][x] = '<';
        mp[H][x + 1] = '>';
        w--;
    }
    
    for(ll y = 1; y + 1 <= H; y += 2){
        for(ll x = 1; x + 1 <= W; x += 2){
            if(h > 1){
                mp[y][x] = '^';
                mp[y][x + 1] = '^';
                mp[y + 1][x] = 'v';
                mp[y + 1][x + 1] = 'v';
                h -= 2;
            }
            else if(w > 1){
                mp[y][x] = '<';
                mp[y][x + 1] = '>';
                mp[y + 1][x] = '<';
                mp[y + 1][x + 1] = '>';
                w -= 2;
            }
            else if(h == 1){
                mp[y][x] = '^';
                mp[y + 1][x] = 'v';
                h--;
            }
            else if(w == 1){
                mp[y][x] = '<';
                mp[y][x + 1] = '>';
                w--;
            }
        }
    }
    if(H >= 3 && W >= 3 && h == 1 && mp[H-1][W-2] == '.' && mp[H-1][W-1] == '.' && mp[H][W-2] == '<' && mp[H][W-1] == '>' && mp[H][W] == '.'){
        h--;
        mp[H-1][W-2] = '^';
        mp[H-1][W-1] = '.';
        mp[H][W-2] = 'v';
        mp[H][W-1] = '<';
        mp[H][W] = '>';
    }
    if(H >= 3 && W >= 3 && w == 1 && mp[H-2][W-1] == '.' && mp[H-2][W] == '^' && mp[H-1][W-1] == '.' && mp[H-1][W] == 'v' && mp[H][W] == '.'){
        w--;
        mp[H-2][W-1] = '<';
        mp[H-2][W] = '>';
        mp[H-1][W-1] = '.';
        mp[H-1][W] = '^';
        mp[H][W] = 'v';
    }
    
    if(h || w){
        cout << "NO" << endl;
    }
    else{
        cout << "YES" << endl;
        rep1(y, H){
            rep1(x, W)cout << mp[y][x];
            cout << endl;
        }        
    }


    return 0;
}
### Prompt

Your challenge is to write a CPP solution to the following 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

### Response

```cpp
//
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<ll, P>IP;
typedef vector<ll> V;
typedef vector<V> V2;
typedef vector<vector<P> > G;
void g_dir(G &graph, ll a, ll b, ll w = 1){graph[a].push_back(P(b, w));}
void g_undir(G &graph, ll a, ll b, ll w = 1){g_dir(graph, a, b, w);g_dir(graph, b, a, w);}
#define rep(i, n) for(ll (i) = 0; (i) < (n); (i)++)
#define rep1(i, n) for(ll (i) = 1; (i) <= (n); (i)++)
#define rrep(i, n) for(ll (i) = (n) - 1; (i) >= 0; (i)--)
#define rrep1(i, n) for(ll (i) = (n); (i) >= 1; (i)--)
template<class T> void chmax(T &a, const T &b){if(a < b){a = b;}}
template<class T> void chmin(T &a, const T &b){if(a > b){a = b;}}
const ll INF = 1145141919;
const ll MOD = 1000000007;
const ll NUM = 101010;

char mp[1010][1010];

int main(){

    ll H, W, w, h;
    cin >> H >> W >> w >> h;
    rep1(y, H)rep1(x, W)mp[y][x] = '.';
    for(ll y = 1; W % 2 && y + 1 <= H && h; y += 2){
        mp[y][W] = '^';
        mp[y + 1][W] = 'v';
        h--;
    }
    for(ll x = 1; H % 2 && x + 1 <= W && w; x += 2){
        mp[H][x] = '<';
        mp[H][x + 1] = '>';
        w--;
    }
    
    for(ll y = 1; y + 1 <= H; y += 2){
        for(ll x = 1; x + 1 <= W; x += 2){
            if(h > 1){
                mp[y][x] = '^';
                mp[y][x + 1] = '^';
                mp[y + 1][x] = 'v';
                mp[y + 1][x + 1] = 'v';
                h -= 2;
            }
            else if(w > 1){
                mp[y][x] = '<';
                mp[y][x + 1] = '>';
                mp[y + 1][x] = '<';
                mp[y + 1][x + 1] = '>';
                w -= 2;
            }
            else if(h == 1){
                mp[y][x] = '^';
                mp[y + 1][x] = 'v';
                h--;
            }
            else if(w == 1){
                mp[y][x] = '<';
                mp[y][x + 1] = '>';
                w--;
            }
        }
    }
    if(H >= 3 && W >= 3 && h == 1 && mp[H-1][W-2] == '.' && mp[H-1][W-1] == '.' && mp[H][W-2] == '<' && mp[H][W-1] == '>' && mp[H][W] == '.'){
        h--;
        mp[H-1][W-2] = '^';
        mp[H-1][W-1] = '.';
        mp[H][W-2] = 'v';
        mp[H][W-1] = '<';
        mp[H][W] = '>';
    }
    if(H >= 3 && W >= 3 && w == 1 && mp[H-2][W-1] == '.' && mp[H-2][W] == '^' && mp[H-1][W-1] == '.' && mp[H-1][W] == 'v' && mp[H][W] == '.'){
        w--;
        mp[H-2][W-1] = '<';
        mp[H-2][W] = '>';
        mp[H-1][W-1] = '.';
        mp[H-1][W] = '^';
        mp[H][W] = 'v';
    }
    
    if(h || w){
        cout << "NO" << endl;
    }
    else{
        cout << "YES" << endl;
        rep1(y, H){
            rep1(x, W)cout << mp[y][x];
            cout << endl;
        }        
    }


    return 0;
}
```