A robot is put at the origin in a two-dimensional plane. Initially, the robot is facing in the positive x-axis direction.

This robot will be given an instruction sequence s. s consists of the following two kinds of letters, and will be executed in order from front to back.

* `F` : Move in the current direction by distance 1.
* `T` : Turn 90 degrees, either clockwise or counterclockwise.



The objective of the robot is to be at coordinates (x, y) after all the instructions are executed. Determine whether this objective is achievable.

Constraints

* s consists of `F` and `T`.
* 1 \leq |s| \leq 8 000
* x and y are integers.
* |x|, |y| \leq |s|

Input

Input is given from Standard Input in the following format:


s
x y


Output

If the objective is achievable, print `Yes`; if it is not, print `No`.

Examples

Input

FTFFTFFF
4 2


Output

Yes


Input

FTFFTFFF
-2 -2


Output

Yes


Input

FF
1 0


Output

No


Input

TF
1 0


Output

No


Input

FFTTFF
0 0


Output

Yes


Input

TTTT
1 0


Output

No
import java.io.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    long MOD = 1_000_000_007;
    int inf = Integer.MAX_VALUE;

    void solve(){
        char[] s = ns().toCharArray();
        int n = s.length;
        int x = ni();
        int y = ni();
        int m = 20000;
        boolean[] dpx = new boolean[2*m+1];
        boolean[] dpy = new boolean[2*m+1];
        int res = 0;
        int dir = 0;
        dpx[m] = true;
        for(int i = 0; i < n; i++){
            boolean[] ndpx = new boolean[2*m+1];
            if(s[i]=='F'){
                res++;
            }
            if((s[i]=='T'||i==n-1)&&res>0){
                if(dir%2==0){
                   for(int j = -n; j <= n; j++){
                        if(dir>0) ndpx[j-res+m] |= dpx[j+m];
                        ndpx[j+res+m] |= dpx[j+m];
                   } 
                   dpx = ndpx;
               }
            }
            if(s[i]=='T'){
                dir++;
                res = 0;
            }
        }
        dir = 0;
        dpy[m] = true;
        for(int i = 0; i < n; i++){
            boolean[] ndpy = new boolean[2*m+1];
            if(s[i]=='F'){
                res++;
            }
            if((s[i]=='T'||i==n-1)&&res>0){
                if(dir%2==1){
                   for(int j = -n; j <= n; j++){
                        ndpy[j-res+m] |= dpy[j+m];
                        ndpy[j+res+m] |= dpy[j+m];
                   } 
                   dpy = ndpy;
               }
            }
            if(s[i]=='T'){
                dir++;
                res = 0;
            }
        }
        if(dpx[x+m] && dpy[y+m]){
            out.println("Yes");
        }
        else out.println("No");
        // for(int i = -n; i <= n; i++){
        //     if(dpx[i+m]>0) out.println(i);
        // }
        // for(int i = -n; i <= n; i++){
        //     if(dpy[i+m]>0) out.println(i);
        // }

    }
    
    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}