A map of some object is a rectangular field consisting of n rows and n columns. Each cell is initially occupied by the sea but you can cover some some cells of the map with sand so that exactly k islands appear on the map. We will call a set of sand cells to be island if it is possible to get from each of them to each of them by moving only through sand cells and by moving from a cell only to a side-adjacent cell. The cells are called to be side-adjacent if they share a vertical or horizontal side. It is easy to see that islands do not share cells (otherwise they together form a bigger island).

Find a way to cover some cells with sand so that exactly k islands appear on the n × n map, or determine that no such way exists. 

Input

The single line contains two positive integers n, k (1 ≤ n ≤ 100, 0 ≤ k ≤ n2) — the size of the map and the number of islands you should form.

Output

If the answer doesn't exist, print "NO" (without the quotes) in a single line.

Otherwise, print "YES" in the first line. In the next n lines print the description of the map. Each of the lines of the description must consist only of characters 'S' and 'L', where 'S' is a cell that is occupied by the sea and 'L' is the cell covered with sand. The length of each line of the description must equal n.

If there are multiple answers, you may print any of them.

You should not maximize the sizes of islands.

Examples

Input

5 2


Output

YES
SSSSS
LLLLL
SSSSS
LLLLL
SSSSS


Input

5 25


Output

NO
import java.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


public class Solution {
    
    static Solution.MyScanner sc = new Solution.MyScanner();
//  static Solution.Parser sc = new Parser(System.in);
    static PrintWriter out = new PrintWriter(System.out, true);

    public static void main(String[] args) throws Exception {
        int n = sc.nextInt(), k = sc.nextInt() ;
        char map[][] = new char[n][n] ;
        for(char[] x : map){
            Arrays.fill(x, 'S');
        }
        int x = -1,y = -1;
        for(int i = 0 ; i < n && k > 0 ; i ++){
            for(int j = (i%2 == 0? 0 : 1) ; j < n && k > 0 ; j += 2){
                map[i][j] = 'L' ;
                x = i;
                y = j;
                k--;
            }
        }
//        for(int i = x ; i < n ; i++){
//            for(int j = y ; j < n ; j++){
//                map[i][j] = 'L' ;
//            }
//        }
//        x += 2;y = 0;
//        for(int i = x ; i < n ; i++){
//            for(int j = y ; j < n ; j++){
//                map[i][j] = 'L' ;
//            }
//        }
        if(k == 0){
            out.println("YES");
            for(int i = 0 ; i < n ; i++){
                for(int j = 0 ; j < n ; j++)
                    out.print(map[i][j]);
                out.println();
            }
        }else{
            out.println("NO");
        }
        
        out.close();
    }


    static private class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public int mod(long x) {
            return (int) x % 1000000007;
        }

        public int mod(int x) {
            return x % 1000000007;
        }

        boolean hasNext() {
            if (st.hasMoreElements())
                return true;
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return st.hasMoreTokens();
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class Parser {
        final private int BUFFER_SIZE = 65536; // 2^16, a good compromise for
                                                // some problems
        private InputStream din; // Underlying input stream
        private byte[] buffer; // Self-maintained buffer
        private int bufferPointer; // Current read position in the buffer
        private int bytesRead; // Effective bytes in the buffer read from the
                                // input stream

        public Parser(InputStream in) {
            din = in;
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        /**
         * Read the next integer from the input stream.
         * 
         * @return The next integer.
         * @throws IOException
         */
        public int nextInt() throws IOException {
            int result = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            while (c >= '0' && c <= '9') {
                result = result * 10 + c - '0';
                c = read();
            }
            if (neg)
                return -result;
            return result;
        }

        /**
         * Read the next byte of data from the input stream.
         * 
         * @return the next byte of data, or -1 if the end of the stream is
         *         reached.
         * @throws IOException
         *             if an I/O error occurs.
         */
        public byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        /**
         * Read data from the input stream into the buffer
         * 
         * @throws IOException
         *             if an I/O error occurs.
         */
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
    }
}