Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

3 4 4 2

Sample Output 1

YES
<><>
^<>^
v<>v

This is one example of a way to place four 1 \times 2 tiles and three 2 \times 1 tiles on a 3 \times 4 grid.

Sample Input 2

4 5 5 3

Sample Output 2

YES
<>..^
^.<>v
v<>.^
<><>v

Sample Input 3

7 9 20 20

Sample Output 3

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
ll gcd(ll a, ll b)
{
	ll c = a % b;
	while (c != 0)
	{
		a = b;
		b = c;
		c = a % b;
	}
	return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y)
{
	if (b == 0)
	{
		x = 1;
		y = 0;
		return a;
	}
	long long d = extGCD(b, a % b, y, x);
	y -= a / b * x;
	return d;
}

struct UnionFind
{
	vector<ll> data;

	UnionFind(int sz)
	{
		data.assign(sz, -1);
	}

	bool unite(int x, int y)
	{
		x = find(x), y = find(y);
		if (x == y)
			return (false);
		if (data[x] > data[y])
			swap(x, y);
		data[x] += data[y];
		data[y] = x;
		return (true);
	}

	int find(int k)
	{
		if (data[k] < 0)
			return (k);
		return (data[k] = find(data[k]));
	}

	ll size(int k)
	{
		return (-data[find(k)]);
	}
};

ll M = 1000000007;

vector<ll> fac(2000011);  //n!(mod M)
vector<ll> ifac(2000011); //k!^{M-2} (mod M)

ll mpow(ll x, ll n)
{
	ll ans = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = ans * x % M;
		x = x * x % M;
		n = n >> 1;
	}
	return ans;
}
ll mpow2(ll x, ll n, ll mod)
{
	ll ans = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = ans * x % mod;
		x = x * x % mod;
		n = n >> 1;
	}
	return ans;
}
void setcomb()
{
	fac[0] = 1;
	ifac[0] = 1;
	for (ll i = 0; i < 2000010; i++)
	{
		fac[i + 1] = fac[i] * (i + 1) % M; // n!(mod M)
	}
	ifac[2000010] = mpow(fac[2000010], M - 2);
	for (ll i = 2000010; i > 0; i--)
	{
		ifac[i - 1] = ifac[i] * i % M;
	}
}
ll comb(ll a, ll b)
{
	if (a == 0 && b == 0)
		return 1;
	if (a < b || a < 0)
		return 0;
	ll tmp = ifac[a - b] * ifac[b] % M;
	return tmp * fac[a] % M;
}
ll perm(ll a, ll b)
{
	if (a == 0 && b == 0)
		return 1;
	if (a < b || a < 0)
		return 0;
	return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a)
{
	long long b = M, u = 1, v = 0;
	while (b)
	{
		long long t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= M;
	if (u < 0)
		u += M;
	return u;
}
ll modinv2(ll a, ll mod)
{
	ll b = mod, u = 1, v = 0;
	while (b)
	{
		ll t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= mod;
	if (u < 0)
		u += mod;
	return u;
}
vector<vector<ll>> mul(vector<vector<ll>> a, vector<vector<ll>> b, int n)
{
	int i, j, k, t;
	vector<vector<ll>> c(n);
	for (i = 0; i < n; i++)
	{
		for (j = 0; j < n; j++)
		{
			t = 0;
			for (k = 0; k < n; k++)
				t = (t + a[i][k] * b[k][j] % M) % M;
			c[i].push_back(t);
		}
	}
	return c;
}

template <typename Monoid>
struct SegmentTree
{
	using F = function<Monoid(Monoid, Monoid)>;

	int sz;
	vector<Monoid> seg;

	const F f;
	const Monoid M1;

	SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1)
	{
		sz = 1;
		while (sz < n)
			sz <<= 1;
		seg.assign(2 * sz, M1);
	}

	void set(int k, const Monoid &x)
	{
		seg[k + sz] = x;
	}

	void build()
	{
		for (int k = sz - 1; k > 0; k--)
		{
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	void update(int k, const Monoid &x)
	{
		k += sz;
		seg[k] = x;
		while (k >>= 1)
		{
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	Monoid query(int a, int b)
	{
		Monoid L = M1, R = M1;
		for (a += sz, b += sz; a < b; a >>= 1, b >>= 1)
		{
			if (a & 1)
				L = f(L, seg[a++]);
			if (b & 1)
				R = f(seg[--b], R);
		}
		return f(L, R);
	}

	Monoid operator[](const int &k) const
	{
		return seg[k + sz];
	}

	template <typename C>
	int find_subtree(int a, const C &check, Monoid &M, bool type)
	{
		while (a < sz)
		{
			Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
			if (check(nxt))
				a = 2 * a + type;
			else
				M = nxt, a = 2 * a + 1 - type;
		}
		return a - sz;
	}

	template <typename C>
	int find_first(int a, const C &check)
	{
		Monoid L = M1;
		if (a <= 0)
		{
			if (check(f(L, seg[1])))
				return find_subtree(1, check, L, false);
			return -1;
		}
		int b = sz;
		for (a += sz, b += sz; a < b; a >>= 1, b >>= 1)
		{
			if (a & 1)
			{
				Monoid nxt = f(L, seg[a]);
				if (check(nxt))
					return find_subtree(a, check, L, false);
				L = nxt;
				++a;
			}
		}
		return -1;
	}

	template <typename C>
	int find_last(int b, const C &check)
	{
		Monoid R = M1;
		if (b >= sz)
		{
			if (check(f(seg[1], R)))
				return find_subtree(1, check, R, true);
			return -1;
		}
		int a = sz;
		for (b += sz; a < b; a >>= 1, b >>= 1)
		{
			if (b & 1)
			{
				Monoid nxt = f(seg[--b], R);
				if (check(nxt))
					return find_subtree(b, check, R, true);
				R = nxt;
			}
		}
		return -1;
	}
};

template <unsigned mod>
struct RollingHash
{
	vector<unsigned> hashed, power;

	inline unsigned mul(unsigned a, unsigned b) const
	{
		unsigned long long x = (unsigned long long)a * b;
		unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
		asm("divl %4; \n\t"
			: "=a"(d), "=d"(m)
			: "d"(xh), "a"(xl), "r"(mod));
		return m;
	}

	RollingHash(const string &s, unsigned base = 10007)
	{
		int sz = (int)s.size();
		hashed.assign(sz + 1, 0);
		power.assign(sz + 1, 0);
		power[0] = 1;
		for (int i = 0; i < sz; i++)
		{
			power[i + 1] = mul(power[i], base);
			hashed[i + 1] = mul(hashed[i], base) + s[i];
			if (hashed[i + 1] >= mod)
				hashed[i + 1] -= mod;
		}
	}

	unsigned get(int l, int r) const
	{
		unsigned ret = hashed[r] + mod - mul(hashed[l], power[r - l]);
		if (ret >= mod)
			ret -= mod;
		return ret;
	}

	unsigned connect(unsigned h1, int h2, int h2len) const
	{
		unsigned ret = mul(h1, power[h2len]) + h2;
		if (ret >= mod)
			ret -= mod;
		return ret;
	}

	int LCP(const RollingHash<mod> &b, int l1, int r1, int l2, int r2)
	{
		int len = min(r1 - l1, r2 - l2);
		int low = -1, high = len + 1;
		while (high - low > 1)
		{
			int mid = (low + high) / 2;
			if (get(l1, l1 + mid) == b.get(l2, l2 + mid))
				low = mid;
			else
				high = mid;
		}
		return (low);
	}
};

using RH = RollingHash<1000000007>;

template <typename T>
struct edge
{
	int src, to;
	T cost;

	edge(int to, T cost) : src(-1), to(to), cost(cost) {}

	edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

	edge &operator=(const int &x)
	{
		to = x;
		return *this;
	}

	operator int() const { return to; }
};

template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T>
using Matrix = vector<vector<T>>;

template <typename G>
struct DoublingLowestCommonAncestor
{
	const int LOG;
	vector<int> dep;
	const G &g;
	vector<vector<int>> table;

	DoublingLowestCommonAncestor(const G &g) : g(g), dep(g.size()), LOG(32 - __builtin_clz(g.size()))
	{
		table.assign(LOG, vector<int>(g.size(), -1));
	}

	void dfs(int idx, int par, int d)
	{
		table[0][idx] = par;
		dep[idx] = d;
		for (auto &to : g[idx])
		{
			if (to != par)
				dfs(to, idx, d + 1);
		}
	}

	void build()
	{
		dfs(0, -1, 0);
		for (int k = 0; k + 1 < LOG; k++)
		{
			for (int i = 0; i < table[k].size(); i++)
			{
				if (table[k][i] == -1)
					table[k + 1][i] = -1;
				else
					table[k + 1][i] = table[k][table[k][i]];
			}
		}
	}

	int query(int u, int v)
	{
		if (dep[u] > dep[v])
			swap(u, v);
		for (int i = LOG - 1; i >= 0; i--)
		{
			if (((dep[v] - dep[u]) >> i) & 1)
				v = table[i][v];
		}
		if (u == v)
			return u;
		for (int i = LOG - 1; i >= 0; i--)
		{
			if (table[i][u] != table[i][v])
			{
				u = table[i][u];
				v = table[i][v];
			}
		}
		return table[0][u];
	}
};

int main()
{
	ll n, m, a, b, i, j;
	char c[1000][1000];
	cin >> n >> m >> a >> b;
	for (i = 0; i < n; i++)
		for (j = 0; j < m; j++)
			c[i][j] = '.';
	ll cn = n, cm = m;
	if (n % 2 == 1)
	{
		for (j = 1; j < m; j += 2)
		{
			if (a > 0)
			{
				c[n - 1][j - 1] = '<';
				c[n - 1][j] = '>';
				a--;
			}
			else
				break;
		}
		n--;
	}
	if (m % 2 == 1)
	{
		for (i = 1; i < n; i += 2)
		{
			if (b > 0)
			{
				c[i - 1][m - 1] = '^';
				c[i][m - 1] = 'v';
				b--;
			}
			else
				break;
		}
		m--;
	}
	for (i = 0; i < n; i += 2)
	{
		for (j = 0; j < m; j += 2)
		{
			if (j + 1 < m && a > 0)
			{
				if (a > 1 && i + 1 < n)
				{
					c[i][j] = '<';
					c[i][j + 1] = '>';
					c[i + 1][j] = '<';
					c[i + 1][j + 1] = '>';
					a -= 2;
				}
				else
				{
					c[i][j] = '<';
					c[i][j + 1] = '>';
					a--;
				}
			}
			else if (i + 1 < n && b > 0)
			{
				if (b > 1 && j + 1 < m)
				{
					c[i][j] = '^';
					c[i + 1][j] = 'v';
					c[i][j + 1] = '^';
					c[i + 1][j + 1] = 'v';
					b -= 2;
				}
				else
				{
					c[i][j] = '^';
					c[i + 1][j] = 'v';
					b--;
				}
			}
		}
	}
	if (a == 0 && b == 0)
	{
		cout << "YES" << endl;
		for (i = 0; i < cn; i++)
		{
			for (j = 0; j < cm; j++)
				cout << c[i][j];
			cout << endl;
		}
	}
	else
		cout << "NO" << endl;
}