C++ :

#include <set>
#include <map>
#include <queue>
#include <ctime>
#include <cmath>
#include <cstdio>
#include <vector>
#include <string>
#include <cctype>
#include <bitset>
#include <cstring>
#include <cstdlib>
#include <utility>
#include <iostream>
#include <algorithm>
#define REP(i,a,b) for(int i=(a);i<=(b);i++)
#define PER(i,a,b) for(int i=(a);i>=(b);i--)
#define RVC(i,S) for(int i=0;i<(S).size();i++)
#define RAL(i,u) for(int i=fr[u];i!=-1;i=e[i].next)
using namespace std;
typedef long long LL;
typedef pair<int,int> pii;
      
template<class T> inline
void read(T& num) {
    bool start=false,neg=false;
    char c;
    num=0;
    while((c=getchar())!=EOF) {
        if(c=='-') start=neg=true;
        else if(c>='0' && c<='9') {
            start=true;
            num=num*10+c-'0';
        } else if(start) break;
    }
    if(neg) num=-num;
}
/*============ Header Template ============*/
 
 
const int BASE=(int)(1e8);
 
struct node {
    int num[1005],top;
     
    node(int x=0) {*this=x;}
 
    int& operator[] (int k) {return num[k];}
 
    inline node operator = (int x) {
        top=0;
        if(!x) num[++top]=0;
        else for(;x;num[++top]=x%BASE,x/=BASE);
        return *this;
    }
 
    inline void modify() {
        int i=1,x=0;
        for(;x || i<=top;i++) {
            if(i>top) num[i]=0;
            x+=num[i]; num[i]=x%BASE;x/=BASE;
        }
        top=max(top,i-1);
        for(;top>1 && !num[top];top--);
    }
 
    inline void print() {printf("%d",num[top]);PER(i,top-1,1) printf("%08d",num[i]);}
};
 
inline node operator + (node a,node b) {
    node c;
    c.top=max(a.top,b.top);
    REP(i,1,c.top) {
        if(i>a.top) a[i]=0;
        if(i>b.top) b[i]=0;
        c[i]=a[i]+b[i];
    }
    c.modify();return c;
}
 
inline node operator - (node a,node b) {
    node c;int x=0;
    c.top=max(a.top,b.top);
    REP(i,1,c.top) {
        if(i>a.top) a[i]=0;
        if(i>b.top) b[i]=0;
        a[i]-=x;x=0;
        if(a[i]<b[i]) x=1;
        c[i]=x*BASE+a[i]-b[i];
    }
    c.modify();return c;
}
 
LL tmp[1005];
inline node operator * (node a,node b) {
    node c;
    c.top=a.top+b.top-1;
    REP(i,1,c.top) tmp[i]=0;
    REP(i,1,a.top) REP(j,1,b.top) tmp[i+j-1]+=1LL*a[i]*b[j];
    LL g=0;
    for(int i=1;i<=c.top || g;i++) {
        if(i>c.top) tmp[i]=0;
        g+=tmp[i];c[i]=g%BASE;g/=BASE;
        c.top=max(c.top,i);
    } return c;
}
 
inline node operator / (node a,int b) {
    node c;c.top=1;
    LL x=0;
    PER(i,a.top,1) {
        x=x*BASE+a[i];
        if(x<b) continue;
        c[i]=x/b;x%=b;
        c.top=max(c.top,i);
    } return c;
}
 
inline int operator % (node a,int b) {
    int c=0;
    PER(i,a.top,1) c=(1LL*c*BASE+a[i])%b;
    return c;
}
 
struct fnode {
    node x,y;
 
    fnode(int _x=0,int _y=1) {
        int d=__gcd(_x,_y);_x/=d;_y/=d;x=_x;y=_y;
    }
 
    fnode(node _x,node _y):x(_x),y(_y) {}
 
    inline void chk() {
        REP(i,2,100) while(x%i==0 && y%i==0) x=x/i,y=y/i;
    }
 
    inline void print() {x.print();putchar('/');y.print();}
};
 
inline fnode operator + (fnode a,fnode b) {
    return fnode(a.x*b.y+a.y*b.x,a.y*b.y);
}
 
inline fnode operator - (fnode a,fnode b) {
    return fnode(a.x*b.y-a.y*b.x,a.y*b.y);
}
 
inline fnode operator * (fnode a,fnode b) {
    return fnode(a.x*b.x,a.y*b.y);
}
 
inline fnode operator / (fnode a,fnode b) {
    return fnode(a.x*b.y,a.y*b.x);
}
 
char s[1005];
int f[1005],g[1005];
fnode K[1005],C[1005];
 
int main() {
    int p,q;
    read(p);read(q);
    scanf("%s",s+1);
    int n=strlen(s+1);
    for(int i=2,j=0;i<=n;i++) {
        while(j && s[i]!=s[j+1]) j=f[j];
        if(s[i]==s[j+1]) j++;f[i]=j;
    }
    REP(i,1,n) {
        g[i]=i;
        while(g[i] && s[i+1]==s[g[i]+1]) g[i]=f[g[i]];
        if(s[i+1]!=s[g[i]+1]) g[i]++;
    }
    fnode H=fnode(p,q),T=fnode(q-p,q),I=fnode(1,1);
    K[0]=fnode(1,1);C[0]=fnode(0,1);
    REP(i,1,n) {
        fnode A=H,B=T;
        if(s[i]=='T') swap(A,B);
        K[i]=(K[i-1]-B*K[g[i-1]])/A;K[i].chk();
        C[i]=(C[i-1]-B*C[g[i-1]]+I)/A;C[i].chk();
    } fnode res=C[n]/K[n];res.print();putchar('\n');
    return 0;
}