Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

FTFFTFFF
4 2

Sample Output 1

Yes

The objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.

Sample Input 2

FTFFTFFF
-2 -2

Sample Output 2

Yes

The objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.

Sample Input 3

FF
1 0

Sample Output 3

No

Sample Input 4

TF
1 0

Sample Output 4

No

Sample Input 5

FFTTFF
0 0

Sample Output 5

Yes

The objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.

Sample Input 6

TTTT
1 0

Sample Output 6

No

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

#pragma region kyopuro_templates
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<stdbool.h>
#include<assert.h>
#include<time.h>
#include<ctype.h>
typedef long long ll;
typedef long double ld;
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define repp(i,l,r,k)for(ll i=(l);i<(r);i+=(k))
#define rrep(i,l,r)for(ll i=(l);i>=(r);i--)
#define INF (1LL<<62)
#define MOD1 1000000007
#define MOD2 998244353
#define MAX_N (1 << 20)
#define YES printf("Yes\n")
#define NO printf("No\n")
#define PN printf("\n")
#define charsize 100005 //10^5+5
#define PI 3.141592653589793238

void swap(ll *a, ll *b){ll c;c=*b;*b=*a;*a= c;}
void cin(ll *n){ scanf("%lld",&(*n)); }
ll max2(ll a,ll b){return a>=b?a:b;}
ll min2(ll a,ll b){return a>=b?b:a;}
ll min3(ll a, ll b, ll c){return (a<=b && a<=c) ? a : b<=c ? b : c;}
ll max3(ll a, ll b, ll c){return (a>=b && a>=c) ? a : b>=c ? b : c;}
ll minn(ll n, ll a[]){ll b=INF;rep(i,0,n) b=min2(b,a[i]);return b;}
ll maxn(ll n, ll a[]){ll b=-INF;rep(i,0,n) b=max2(b,a[i]);return b;}
ll POW(ll a, ll b){ll c=1;rep(i,0,b) c*=a;return c;}
double POW_d(double a, double b){double c=1;rep(i,0,b) c*=a;return c;}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
ll mod_MOD1(ll n){n+= n<0?((-n)/MOD1+1)*MOD1:0; return n%=MOD1;}
ll mod_p(ll n ,ll p){n+= n<0?((-n)/p+1)*p:0; return n%=p;}
ll change_into_num(char s[] , ll len, ll p){ return !p ? 0 : POW(10,p-1)*(s[len-p]-'0') + change_into_num(s,len,p-1); }
ll digits(ll a, ll b){return a/b?1+digits(a/b,b):1;}
ll base(ll n, ll a, ll i){return i==1?n%a:base(n/a,a,i-1);}
ll is_inArr1(ll x, ll n){ return ( x<0 || x>=n ) ? 0 : 1 ; }
ll is_inArr2(ll y, ll x, ll h, ll w){ return ( y<0 || y>=h || x<0 || x>=w ) ? 0 : 1 ; }


void lr_lower( int *l, int *r, ll am, ll val , int type ){ (type<3) ? ( am < val ?  ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ) : ( am <= val ? ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ); }
void lr_upper( int *l, int *r, ll am, ll val , int type ){ (type<3) ? ( am <= val ?  ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ) : ( am < val ? ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ); }
int cmp_lower( ll a, ll b, int type ){ return (type==1) ? ( a==b ? 1 : 0 ) : (type==2) ? ( a>=b ? 1 : 0 ) : ( a>b ? 1 : 0 ) ; }
int cmp_upper( ll a, ll b, int type ){ return (type==1) ? ( a==b ? 1 : 0 ) : (type==2) ? ( a<=b ? 1 : 0 ) : ( a<b ? 1 : 0 ) ; }
// return smallest p  which meets  a[p]==val :1  >=:2   >:3
ll lower_bound( ll a[], int l, int r, ll val , int type ){  while(r-l>1) lr_lower(&l,&r,a[ (l+r)/2 ],val,type);  return cmp_lower(a[l],val,type) ? l : cmp_lower(a[r],val,type) ? r : -1;  }
// return biggest p  which meets   a[p]==val :1  <=:2   <:3
ll upper_bound( ll a[], int l, int r, ll val , int type ){  while(r-l>1) lr_upper(&l,&r,a[ (l+r)/2 ],val,type); return cmp_upper(a[r],val,type) ? r : cmp_upper(a[l],val,type) ? l : -1; }
// count i  which meets ai==x
ll count(ll a[], int l, int r, ll x){  int p = lower_bound(a,l,r,x,1);  return p==-1 ? 0 : upper_bound(a,p,r,x,1)-p+1; }

ll *factors[2] , fac_cnt=0 , is_factor_prepared=0;
ll factor_pre(){  rep(i,0,1){ if(is_factor_prepared++) return 0; }  ll tmp=(1e6)/2+1, fac_tmp[tmp];  rep(i,0,tmp){fac_tmp[i]=i?2*i+1:2;}  rep(i,1,tmp){if(fac_tmp[i]){  repp(j,3,tmp/(2*i+1)+1,2 ){  if( j*(2*i+1)<tmp ) fac_tmp[ (j*(2*i+1)-1)/2 ]=0;  }  }else continue;}  rep(i,0,tmp){if(fac_tmp[i]){  rep(j,0,2){ factors[j] = realloc( factors[j] , sizeof(ll)*( fac_cnt +1 ) );  factors[j][j?fac_cnt++:fac_cnt]=j?0:fac_tmp[i];  }  } }  return 0;  }
ll factor(ll n, ll new_common_plus){ factor_pre();  rep(i,0,fac_cnt){ ll cnt=0; rep(j,0,1){ while( ( cnt+= n %factors[0][i]==0 ? 1 : 0 )  && (n/=factors[0][i]) %factors[0][i]==0 ) continue; } factors[1][i]= new_common_plus==1 ? cnt :  new_common_plus==2 ? max2(factors[1][i],cnt) : factors[1][i]+cnt ;  if( factors[0][i]> n ) break; } return n; }
ll judge_prime(ll n){ factor_pre(); rep(i,0,fac_cnt){ if(n<factors[0][i]*factors[0][i] || n==factors[0][i]) break; else if(n%factors[0][i]==0) n/=n; }  return n==1?0:1; }

ll *mf_arr,*inv_arr,*finv_arr,is_minv_made=0,is_mf_made=0,num_of_inv=2*1e6+10;
ll makeinv(ll n , ll mod){  rep(i,0,1){if(is_minv_made++) return 0;}  inv_arr = realloc(inv_arr, sizeof(ll)*2 );  finv_arr = realloc(finv_arr, sizeof(ll)*2 );  inv_arr[1]=1;finv_arr[0]=finv_arr[1]=1;  rep(i,2,n+1){  inv_arr = realloc(inv_arr, sizeof(ll)*(i+1) );  finv_arr = realloc(finv_arr, sizeof(ll)*(i+1) );  inv_arr[i]= mod - inv_arr[mod%i] * (mod / i) % mod;  finv_arr[i] = finv_arr[i - 1] * inv_arr[i] % mod;  }  return 0; }
ll make_mf(ll n, ll mod){  rep(i,0,1){ if(is_mf_made++) return 0; }  mf_arr = realloc(mf_arr, sizeof(ll)*2 );  ll x=1;  mf_arr[0]=mf_arr[1]=x;  rep(i,2,n+1){   x=x*i%mod;  mf_arr = realloc(mf_arr, sizeof(ll)*(i+1) );  mf_arr[i]=x; }  return 0;  }
ll m_inv(ll x, ll mod, ll is_fac ){ makeinv(num_of_inv,mod);  return is_fac?finv_arr[x]:inv_arr[x]; }
ll m_f(ll x, ll mod){  make_mf(num_of_inv,mod);  return mf_arr[x];  }
ll mod_nck(ll n, ll k, ll mod){ return m_f(n,mod)*m_inv(k,mod,1)%mod*m_inv(n-k,mod,1)%mod; }
ll m_p(ll r,ll n,ll mod){  ll t=1,s=r;  while(n>0){ t = (n&1) ? t*s%mod : t;  s=s*s%mod; n>>=1; }  return r?t:0;  }
ll m_mul2(ll a, ll b, ll mod){ return a*b%mod; }
ll m_mul3(ll a, ll b, ll c, ll mod){ return m_mul2(a*b%mod,c,mod); }
ll m_mul4(ll a, ll b, ll c, ll d, ll mod){ return m_mul3(a*b%mod,c,d,mod); }
ll m_mul5(ll a, ll b, ll c, ll d, ll e, ll mod){ return m_mul4(a*b%mod,c,d,e,mod); }

int upll(const void*a, const void*b){return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;}
int downll(const void*a, const void*b){return*(ll*)a<*(ll*)b?1:*(ll*)a>*(ll*)b?-1:0;}
int cmp_string( const void * a , const void * b ) {  return strcmp( (char *)a , (char *)b ); }  // qsort((void*)s,n,sizeof(s[0]),int_sort );
int cmp_char(const void * a, const void * b) { return *(char *)a - *(char *)b;}
void sortup(ll*a,int n){qsort(a,n,sizeof(ll),upll);}
void sortdown(ll*a,int n){qsort(a,n,sizeof(ll),downll);}
void sort_string(int n,int size,char s[][size]){ qsort( (void*)s , n , sizeof(s[0]) , cmp_string ); }
void sort_char(char *s){ qsort( (void *)s , strlen(s) , sizeof(char) , cmp_char ); }
ll unique_string(ll n ,ll size, char s[][size]){ ll ans=1; rep(i,1,n) if( strcmp(s[i],s[i-1]) ) ans++; return ans; }
ll unique_num(ll n , ll a[]){ ll ans=1; rep(i,1,n) if( a[i]!=a[i-1] ) ans++; return ans; }

typedef struct{ ll a , b;}fr;
int cmp1( const void *p, const void *q ) { return ((fr*)p) ->a - ((fr*)q)->a;}
int cmp2( const void *p, const void *q ) { return ((fr*)q) ->a - ((fr*)p)->a;}
void strsortup(fr*a,int n){qsort(a,n,sizeof(fr),cmp1);}
void strsortdown(fr*a,int n){qsort(a,n,sizeof(fr),cmp2);}

#pragma region AVL
/*---------------------------AVL start--------------------------------*/
//https://qiita.com/mikecat_mixc/items/e9f8248de2ae7f7a0a29
typedef struct node_AVL_set{  
    ll val;
    int diff;
    int cnt;
    struct node_AVL_set *child[2];
}AVL_set;
void AVL_set_inside_rotate(AVL_set **node, int is_right){
    int l = is_right==false , r = is_right==true , sign = is_right ? 1 : -1;
    if((*node)->child[l] != NULL){
        AVL_set* left = (*node)->child[l];
        int a= (*node)->diff * sign , b= left->diff * sign ,na,nb;
        if(b+1){
            na=a-1-b;
            nb= (a-b) ? b-1 : a-2;
        }else{
            na=a-1;
            nb= a ? b-1 : a+b-2;
        }
        (*node)->diff = na * sign;
        left->diff = nb * sign;
        /* rotate-> */
        (*node)->child[l] = (*node)->child[l]->child[r];
        left->child[r] = *node;
        *node = left;
    }
}
int AVL_set_inside_update(AVL_set **node, ll data, int add){
    if(*node == NULL){
        if(add==2){
            *node = malloc(sizeof(AVL_set));
            (*node)->val = data;
            (*node)->cnt = 1;
            (*node)->diff = 0;
            (*node)->child[0] = NULL;
            (*node)->child[1] = NULL;
        }
        return add==2 ? *node != NULL : 0; 
    }else{
        int l, delta, delta_sign; AVL_set *next_node;
        if(data == (*node)->val){
            if(add==2){
                (*node)->cnt++;
                return 0;
            }else{
                if( add && (*node)->cnt > 1 ){
                    (*node)->cnt--; return 0;
                }else{
                    if((*node)->child[1] == NULL){
                        next_node = (*node)->child[0];
                        free(*node);
                        *node = next_node;
                        return -1;
                    }else if((*node)->child[0] == NULL){
                        next_node = (*node)->child[1];
                        free(*node);
                        *node = next_node;
                        return -1;
                    }else{
                        for(next_node = (*node)->child[0];
                        next_node->child[1] != NULL;
                        next_node = next_node->child[1]);
                        (*node)->val = next_node->val;
                        l=0;
                        delta_sign=1;
                        delta = AVL_set_inside_update(&(*node)->child[l], next_node->val, add);
                    }
                }
            }
        }else{
            l = data >= (*node)->val ? 1 : 0;
            delta_sign = data < (*node)->val ? 1 : -1;
            delta = AVL_set_inside_update(&(*node)->child[l], data, add);
        }
        if( delta ){
            int orig_diff = (*node)->diff;
            int do_rotate = 0, rotate_l , diff_sign , rotate_right;
            (*node)->diff += delta * delta_sign;
            if((*node)->diff > 1){
                do_rotate = 1;
                rotate_l = 0;
                diff_sign = 1;
                rotate_right = 1;
            }else if((*node)->diff < -1){
                do_rotate = 1;
                rotate_l = 1;
                diff_sign = -1;
                rotate_right = 0;
            }
            if(do_rotate){
                int child_diff = (*node)->child[rotate_l]->diff;
                if((*node)->child[rotate_l]->diff * diff_sign < 0){
                    AVL_set_inside_rotate(&(*node)->child[rotate_l], !rotate_right);
                }
                AVL_set_inside_rotate(node, rotate_right);
                return delta < 0 && child_diff != 0 ? -1 : 0;
            }
            if     (delta > 0 && orig_diff == 0) return 1;
            else if(delta < 0 && orig_diff != 0) return -1;
            else                                 return 0;
        }else{ 
            return 0;
        }
    }
}

void AVL_set_inside_print(const AVL_set *node, int depth){
    if(node == NULL) return;
    AVL_set_inside_print(node->child[1], depth + 1);
    printf("%lld %d\n", node->val,node->cnt);
    AVL_set_inside_print(node->child[0], depth + 1);    
}
void AVL_set_inside_free(AVL_set *node){
    if(node == NULL) return;
    AVL_set_inside_free(node->child[0]);
    AVL_set_inside_free(node->child[1]);
    free(node);
}
ll AVL_set_inside_count(AVL_set *root, ll val){
    AVL_set *node; node = root;
    while(node){
        if     (val < node->val) node = node->child[0];
        else if(val > node->val) node = node->child[1];
        else                     return node->cnt;
    }
    return 0;
}
ll AVL_set_inside_minmax(AVL_set *root, int type){
    while(root->child[type] !=NULL)  root= root->child[type];
    return root->val;
}
void AVL_set_inside_swap(AVL_set **node1, AVL_set **node2){  
    AVL_set *tmp;  tmp=*node1; *node1=*node2; *node2=tmp;
}

#define set_MAX_SIZE 514511
ll set_main( int command , int set_num , ll val ){
    static bool set_is_init=false;
    static AVL_set *set_pointer[set_MAX_SIZE];
    static ll set_siz[set_MAX_SIZE];
    if(!set_is_init){ set_is_init=true; rep(i,0,set_MAX_SIZE){ *(set_pointer+i) = NULL; set_siz[i]=0; } }
    if(command==-1){ AVL_set_inside_print( set_pointer[set_num] ,0); }
    if(command==1){ AVL_set_inside_count(set_pointer[set_num],val) ? 1 : set_siz[set_num]++;  AVL_set_inside_update( &set_pointer[set_num] , val , 2 ); }
    if(command==2){ return AVL_set_inside_count(set_pointer[set_num],val); }
    if(command==3){ ( AVL_set_inside_count(set_pointer[set_num],val) > 1 ) ? 1 : set_siz[set_num]--;  AVL_set_inside_update( &set_pointer[set_num] , val,1); }
    if(command==4){ set_siz[set_num]--; AVL_set_inside_update( &set_pointer[set_num] , val , 0 ); }
    if(command==5){ set_siz[set_num]=0; AVL_set_inside_free( set_pointer[set_num] ); set_pointer[set_num] = NULL; }
    if(command==6){ return set_siz[set_num]; }
    if(command==7){ return AVL_set_inside_minmax(set_pointer[set_num],1); }
    if(command==8){ return AVL_set_inside_minmax(set_pointer[set_num],0); }
    if(command==9){ AVL_set_inside_swap(&set_pointer[set_num],&set_pointer[val]); }
    return 0;
}

void set_print(int set_num){ set_main(-1,set_num,0); }
void set_insert(int set_num, ll val){ set_main(1,set_num,val); }
ll set_count(int set_num, ll val){ return set_main(2,set_num,val); }
void set_erase(int set_num, ll val, int is_all){ if(is_all) set_main(4,set_num,val); else set_main(3,set_num,val); }
void set_clear(int set_num){ set_main(5,set_num,0); }
ll set_size(int set_num){ return set_main(6,set_num,0); }
ll set_max(int set_num){ return set_main(7,set_num,0); }
ll set_min(int set_num){ return set_main(8,set_num,0); }
void set_swap(ll set_num1, ll set_num2){ set_main(9,set_num1,set_num2); }

/*
insert *
size *
clear *
erase *
count *
max *
min *
swap *
begin
end
merge  source の要素のキーと等価なキーの要素がある場合、その要素は source から抽出されない
lower_bound
upper_bound
*/

// ll map_main()

/*---------------------------AVL start--------------------------------*/

#pragma endregion AVL



#pragma endregion kyopuro_templates













char s[1151154];
ll w[2][25525];
ll h[2][25525];
ll q[11511];
void solve(){
    // fgets(s,sizeof(s),stdin); 
    ll n,x,y;
    // ll ans=0;
    scanf("%s",s);
    n=strlen(s);
    cin(&x);
    cin(&y);
    ll lr=0,ud=0,qcnt=0,t=1;
    rep(i,0,n){
        if(s[i]=='T'){
            q[qcnt++]=0;
            t^=1;
        }else{
            if(qcnt && q[qcnt-1]){
                q[qcnt-1]++; 
            }else{
                q[qcnt++]=1;
            }
            if(t){
                lr++;
            }else{
                ud++;
            }
        }
    }
    t=1;
    ll center=1e4;
    w[0][center]=1;
    h[0][center]=1;
    ll cntw=0,cnth=0,qh=0,qw=0,second=0;
    // rep(i,0,qcnt){
    //     printf("%lld ",q[i]);
    // }PN;
    rep(i,0,qcnt){
        if(q[i]==0){
            t^=1; second=1;
        }else{
            // printf("%lld\n",t);
            if(t){
                qw++;
                rep(j,-lr-5+center,lr+5+center){
                    if( w[cntw][j] ){
                        // printf("%lld %lld\n",i,j);
                        if(second) w[cntw^1][j-q[i]]=1;
                        w[cntw^1][j+q[i]]=1;
                        w[cntw][j]=0;
                    }
                }
                cntw^=1;
            }else{
                qh++;
                rep(j,-ud-5+center,ud+5+center){
                    if( h[cnth][j] ){
                        // printf("%lld %lld\n",i,j);
                        h[cnth^1][j-q[i]]=1;
                        h[cnth^1][j+q[i]]=1;
                        h[cnth][j]=0;
                    }
                }
                cnth^=1;
            }
            // rep(j,-8+center,8+center){
            //     printf("%lld ",w[cntw][j]);
            // }PN;
            // rep(j,-8+center,8+center){
            //     printf("%lld ",h[cnth][j]);
            // }PN; PN;
        }        
    }
    if( w[qw%2][center+x] && h[qh%2][center+y] ){
        YES;
    }else NO;
}

int main(void){
    ll T=1;
    // cin(&T);
    rep(i,0,T){ solve(); }
    return 0;
}


/*
    while (ng + 1 < ok) {
        int p = ng + (ok - ng) / 2;
        int cnt = 0;
        for (i = 0; i < n; i++) {
            cnt += (a[i] + p - 1) / p - 1;
        }
        if (cnt <= k) ok = p; else ng = p;
    }
*/
// 10^18 2^60 3^38 5^26