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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    // const int M = 998244353;
    const long LM = (long)1e18;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    static void Main(string[] args)
    {
        int n, m, a, b;
        sc.Multi(out n, out m, out a, out b);
        var ans = new char[n][];
        for (int i = 0; i < n; i++)
        {
            ans[i] = new string('.', m).ToCharArray();
        }
        if (n % 2 == 1) {
            for (int i = m % 2; i + 1 < m; i += 2)
            {
                if (a > 0) {
                    --a;
                    ans[n - 1][i    ] = '<';
                    ans[n - 1][i + 1] = '>';
                }
            }
        }
        if (m % 2 == 1) {
            for (int i = 0; i + 1 < n; i += 2)
            {
                if (b > 0) {
                    --b;
                    ans[i    ][m - 1] = '^';
                    ans[i + 1][m - 1] = 'v';
                }
            }
        }
        for (int i = 0; i + 1 < n; i += 2)
        {
            for (int j = 0; j + 1 < m; j += 2)
            {
                if (a > 0) {
                    --a;
                    ans[i    ][j    ] = '<';
                    ans[i    ][j + 1] = '>';
                    if (a > 0) {
                        --a;
                        ans[i + 1][j    ] = '<';
                        ans[i + 1][j + 1] = '>';
                    }
                }
                else if (b > 0) {
                    --b;
                    ans[i    ][j    ] = '^';
                    ans[i + 1][j    ] = 'v';
                    if (b > 0) {
                        --b;
                        ans[i    ][j + 1] = '^';
                        ans[i + 1][j + 1] = 'v';
                    }
                }
            }
        }
        if (a > 0 && ans[0][m - 2] == '.' && ans[0][m - 1] == '.') {
            --a;
            ans[0][m - 2] = '<';
            ans[0][m - 1] = '>';
        }
        if (a == 0 && b == 0) {
            Prt("YES");
            foreach (var item in ans)
            {
                Prt(new string(item));
            }
        }
        else {
            Prt("NO");
        }
        sw.Flush();
    }
    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));
}
class pair<T, U> : IComparable<pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T v1;
    public U v2;
    public pair(T v1, U v2) {
        this.v1 = v1;
        this.v2 = v2;
    }
    public int CompareTo(pair<T, U> a) => v1.CompareTo(a.v1) != 0 ? v1.CompareTo(a.v1) : v2.CompareTo(a.v2);
    public override string ToString() => v1 + " " + v2;
}
static class util
{
    public static pair<T, T> make_pair<T>(this IList<T> l) where T : IComparable<T> => make_pair(l[0], l[1]);
    public static pair<T, U> make_pair<T, U>(T v1, U v2) where T : IComparable<T> where U : IComparable<U> => new pair<T, U>(v1, v2);
    public static T sqr<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    public static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan
{
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => Console.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() where T : IComparable<T> where U : IComparable<U>
    { T a; U b; Multi(out a, out b); return make_pair(a, b); }
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new []{' '}, System.StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
}
static class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a) {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n) {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n) {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n) {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static double[][] dE(int n) {
        var ret = new double[n][];
        for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n) {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double[][] pow(double[][] A, long n) {
        if (n == 0) return dE(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double dot(double[] x, double[] y) {
        int n = x.Length;
        double ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static double _dot(double[] x, double[] y) {
        int n = x.Length;
        double ret = 0, r = 0;
        for (int i = 0; i < n; i++) {
            double s = ret + (x[i] * y[i] + r);
            r = (x[i] * y[i] + r) - (s - ret);
            ret = s;
        }
        return ret;
    }
    public static long dot(long[] x, long[] y) {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static T[][] trans<T>(T[][] A) {
        int n = A[0].Length, m = A.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
        return ret;
    }
    public static double[] mul(double a, double[] x) {
        int n = x.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = a * x[i];
        return ret;
    }
    public static long[] mul(long a, long[] x) {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = a * x[i] % Mod;
        return ret;
    }
    public static double[] mul(double[][] A, double[] x) {
        int n = A.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[] mul(long[][] A, long[] x) {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static double[][] mul(double a, double[][] A) {
        int n = A.Length;
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(a, A[i]);
        return ret;
    }
    public static long[][] mul(long a, long[][] A) {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(a, A[i]);
        return ret;
    }
    public static double[][] mul(double[][] A, double[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y) {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B) {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b) {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) => pow(a, Mod - 2);
    public static long gcd(long a, long b) {
        while (b > 0) { var t = a % b; a = b; b = t; } return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y) {
        long g = a; x = 1; y = 0;
        if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
        return g;
    }
    public static long lcm(long a, long b) => a / gcd(a, b) * b;

    static long[] facts;
    public static long[] setfacts(int n) {
        facts = new long[n + 1];
        facts[0] = 1;
        for (int i = 0; i < n; i++) facts[i + 1] = facts[i] * (i + 1) % Mod;
        return facts;
    }
    public static long comb(int n, int r) {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        if (facts != null && facts.Length > n) return facts[n] * inv(facts[r]) % Mod * inv(facts[n - r]) % Mod;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++) {
            int piv = denom[p - 1];
            if (piv > 1) {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
    public static long[][] getcombs(int n) {
        var ret = new long[n + 1][];
        for (int i = 0; i <= n; i++) {
            ret[i] = new long[i + 1];
            ret[i][0] = ret[i][i] = 1;
            for (int j = 1; j < i; j++) ret[i][j] = (ret[i - 1][j - 1] + ret[i - 1][j]) % Mod;
        }
        return ret;
    }
    // nC0, nC2, ..., nCn
    public static long[] getcomb(int n) {
        var ret = new long[n + 1];
        ret[0] = 1;
        for (int i = 0; i < n; i++) ret[i + 1] = ret[i] * (n - i) % Mod * inv(i + 1) % Mod;
        return ret;
    }
}