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 double ld;
typedef long long ll;
typedef pair<double, double> pdd;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<int, int> pii;
typedef vector<pii> vii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
//const int mod = ;

int main() {
  std::ios::sync_with_stdio(false); std::cin.tie(0);
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  vs res(n, string(m, '.'));
  if (n % 2) {
    for (int i = 0; i + 1 < m && a > 0; i += 2) {
      res[n-1][i] = '<';
      res[n-1][i+1] = '>';
      --a;
    }
  }
  if (m % 2) {
    for (int i = (res[n-1][m-1] == '.' ? n - 1 : n - 2); i >= 1 && b > 0; i -= 2) {
      res[i-1][m-1] = '^';
      res[i][m-1] = 'v';
      --b;
    }
  }
  int s = (n - n % 2) * (m - m % 2), need = 2 * a + 2 * b;
  bool eq = s == need && a % 2 && b % 2;
  bool ok1 = m > 1 && m % 2 && res[0][m-1] == '.';
  bool ok2 = n > 1 && n % 2 && res[n-1][m-1] == '.';
  if (s < need || (eq && !ok1 && !ok2)) {
    cout << "NO\n"; return 0;
  }
  if (eq) {
    if (ok1) {
      res[0][m-2] = '<'; res[0][m-1] = '>';
      res[0][m-3] = '^'; res[1][m-3] = 'v';
    } else if (ok2) {
      res[n-2][m-1] = '^'; res[n-1][m-1] = 'v';
      res[n-3][m-2] = '<'; res[n-3][m-1] = '>';
    }
    --a; --b;
  }
  for (int i = 0; i + 1 < n; i += 2) for (int j = 0; j + 1 < m; j += 2) {
    if (res[i][j] != '.' || res[i][j+1] != '.' || res[i+1][j] != '.' || res[i+1][j+1] != '.') continue;
    if (a) {
      for (int l = 0; l < 2 && a; ++l) {
        res[i + l][j] = '<';
        res[i + l][j+1] = '>';
        --a;
      }
    } else if (b) {
      for (int l = 0; l < 2 && b; ++l) {
        res[i][j + l] = '^';
        res[i+1][j + l] = 'v';
        --b;
      }
    }
  }
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << res[i] << endl;
  return 0;
}