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: Runtime Error)

#include <bits/stdc++.h>
#define F first
#define S second
#define dq deque
#define vc vector
#define INF (0x3f3f3f3f)
#define LINF ((long long)(0x3f3f3f3f3f3f3f3f))
#define Pb push_back
#define Mp make_pair
#define ll long long
#define _tp template
#define _tyn typename
#define Pf push_front
#define itor iterator
#define sint short int
#define ull unsigned ll
#define pii pair<int,int>
#define uint unsigned int
#define All(x) x.begin(),x.end()
#define B cout << "BreakPoint" << endl;
#define Ms(_data) memset(_data,0,sizeof(_data))
#define Fin(_filename) freopen(_filename,"r",stdin)
#define Fout(_filename) freopen(_filename,"w",stdout)
#define Msn(_data,_num) memset(_data,_num,sizeof(_data))
#define Fastio ios_base::sync_with_stdio(false);cin.tie(0);
#define O_(x) cout << #x << " " << x << "  ";
#define O(x) cout << #x << " " << x << endl;
using namespace std;
#define Mymax(a,b) if(a<b) a = b;
#define Mymin(a,b) if(a>b) a = b;
void Print(int _x){printf("%d\n",_x);}
void Print(ll _x){printf("%lld\n",_x);}
_tp<_tyn T>void Print( T _a[] , int _s , int _t ){
    for( int i = _s ; i <= _t ; i++ )
        cout << _a[i] << " ";
   	cout << endl;
}
#define il inline
#define rg register
struct InputReader{
	static const int bs = 100000;
    char buf[bs];
    int p;
    il InputReader():p(bs) {}
    il void Flush(){
        p = 0;
        fread(buf, 1, bs, stdin);
    }
    il char C(){
        if(p >= bs) Flush();
        return buf[p++];
    }
    int Getnum(){
        char ch = C();
        while( ch < '0'  ||  ch > '9' ) ch = C();
        return (int)(ch-'0');
    }
    il int operator() (){
        int ans = 0;
        char ch = C();
        int fu = 1;
        while( ch < '0'  ||  ch > '9' ){
            if( ch == '-' ) fu = -1;
            ch = C();
        }
        while( ch >= '0'  &&  ch <= '9' ){
            ans *= 10;
            ans += ch-'0';
            ch = C();
        }
        return ans * fu;
    }
    ll Readll(){
        ll ans = 0LL;
        ll fu = 1;
        char ch = C();
        while( ch < '0'  ||  ch > '9' ){
            if( ch == '-' ) fu = -1;
            ch = C();
        }
        while( ch >= '0'  &&  ch <= '9' ){
            ans *= 10LL;
            ans += ch-'0';
            ch = C();
        }
        return ans * fu;
    }
    il void Readstring( string &x ){
        x.clear();
        char ch = C();
        while( !isdigit(ch)  &&  !isalpha(ch) ) ch = C();
        while( isdigit(ch)  ||  isalpha(ch) ){
            x += ch;
            ch = C();
        }
        //x += '\0';
    }
    il void Readalpha( char &c ){
        c = C();
        while( !isalpha(c) ) c = C();
    }
    il char Specialread(){
        char ch = C();
        while( !isalpha(ch) ) ch = C();
        return ch;
    }
}In;
il void Read( int &x ){ x = In(); }
il void Read( int &x, int &y ){ x = In(); y = In(); }
il void Read( int &x1 , int &x2 , int &x3 ){
    x1 = In(); x2 = In(); x3 = In();
}
il void Read( int &x1 , int &x2 , int &x3 , int &x4 ){
    x1 = In(); x2 = In(); x3 = In(); x4 = In();
}
il void Read( ll &x ){
    x = In.Readll();
}
il void Read( ll &x, ll &y ){ x = In.Readll(); y = In.Readll(); }
il void Read( ll &x1 , ll &x2 , ll &x3 ){
    x1 = In.Readll(); x2 = In.Readll(); x3 = In.Readll();
}
il void Read( ll &x1 , ll &x2 , ll &x3 , ll &x4 ){
    x1 = In.Readll(); x2 = In.Readll(); x3 = In.Readll(); x4 = In.Readll();
}
clock_t _starttime , _endtime;
il void FILEIO(){
    #ifdef WIN32
        _starttime = clock();
        Fin("in.in");
    #endif
}
#ifdef WIN32
    #include <windows.h>
    #include <psapi.h>
#endif
il void END(){
    #ifdef WIN32
        _endtime = clock();
        double _timeuse = (_endtime-_starttime)* 1000.0 / CLOCKS_PER_SEC;
        printf("\n\nTime usage:\n%.0lf ms\n",_timeuse);
        HANDLE _handle = GetCurrentProcess();
        PROCESS_MEMORY_COUNTERS pmc;
        GetProcessMemoryInfo(_handle,&pmc,sizeof(pmc));
        double _memuse = pmc.PeakPagefileUsage/1024.00/1024.00;
        printf("Memory usage:\n%.1lf MB\n\n",_memuse);
    #endif
    exit(0);
}
#define For(i,j) for( rg int (i) = 1 ; (i) <= (j) ; (i)++ )
#define For0(i,j) for( rg int (i) = 0 ; (i) < (j) ; (i)++ )
#define Forx(i,j,k) for( rg int (i) = (j) ; (i) <= (k) ; (i)++ )
#define Forstep(i,j,k,st) for( rg int (i) = (j) ; (i) <= (k) ; (i) += (st) )
#define fOR(i,j) for( rg int (i) = (j) ; (i) >= 1 ; (i)-- )
#define fOR0(i,j) for( rg int (i) = (j)-1 ; (i) >= 0 ; (i)-- )
#define fORx(i,j,k) for( rg int (i) = (k) ; (i) >= (j) ; (i)-- )
int dx[] = {0,-1,0,1};
int dy[] = {1,0,-1,0};
//			D L U  R
#define Mymod(a,b) if( a >= b ) a -= b;
#define Rmod(a,b) a = (a%b+b)%b
/////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////
#define MAXN 3010
il void GG(){
    cout << "NO" << endl;
    END();
}

int n,m,nn,mm;
int a,b;
char ans[MAXN][MAXN];

il void Pr(){
    For(i,nn){
        For(j,mm)
            cout << ans[i][j];
        cout << endl;
    }
}

int main(){
	FILEIO();

    Read(n,m,a,b);
    nn = n; mm = m;
    if( a*2 + b*2 > n*m ) GG();
    For(i,nn)
        For(j,mm)
            ans[i][j] = '.';

    if(m&1){
        for( int i = 1 ; i+1 <= n  &&  b ; i += 2 ){
            b--;
            ans[i][m] = '^';
            ans[i+1][m] = 'v';
        }
        m--;
    }

    int pos = 1;
    int i = 1;
    while(b){
        if( pos+1 > n ) GG();
        for( i = 1 ; i <= m  &&  b ; i++ ){
            ans[pos][i] = '^';
            ans[pos+1][i] = 'v';
            b--;
        }
        pos += 2;
    }

    pos -= 2;
    int ii = i;
    for( ; i+1 <= m  &&  a ; i += 2 ){
        ans[pos][i] = '<';
        ans[pos][i+1] = '>';
        a--;
    }

    pos++;
    if( pos > n ) GG();
    for( i = ii ; i+1 <= m  &&  a ; i += 2 ){
        ans[pos][i] = '<';
        ans[pos][i+1] = '>';
        a--;
    }

    pos++;
    while(a){
        if( pos > n ) GG();
        for( i = 1 ; i+1 <= m  &&  a ; i += 2 ){
            ans[pos][i] = '<';
            ans[pos][i+1] = '>';
            a--;
        }
        pos++;
    }
    if( a || b ) GG();

    cout << "YES" << endl;
    Pr();

	END();
}