#include <bits/stdc++.h>
using namespace std;
#define rep(i, n)  for(long long i=0;i<(long long)(n);i++)
#define REP(i,k,n) for(long long i=k;i<(long long)(n);i++)
#define all(a) a.begin(),a.end()
#define pb emplace_back
#define eb emplace_back
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
#define ub(v,k) (upper_bound(all(v),k)-v.begin())
#define fi first
#define se second
#define pi M_PI
#define PQ(T) priority_queue<T>
#define SPQ(T) priority_queue<T,vector<T>,greater<T>>
#define dame(a) {out(a);return 0;}
#define decimal cout<<fixed<<setprecision(15);
#define dupli(a) a.erase(unique(all(a)),a.end())
typedef long long ll;
typedef pair<ll,ll> P;
typedef tuple<ll,ll,ll> PP;
typedef tuple<ll,ll,ll,ll> PPP;
typedef multiset<ll> S;
using vi=vector<ll>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vvvvi=vector<vvvi>;
using vp=vector<P>;
using vvp=vector<vp>;
using vb=vector<bool>;
using vvb=vector<vb>;
const ll inf=1001001001001001001;
const ll INF=1001001001;
const ll mod=1000000007;
const double eps=1e-10;
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<'\n';}
template<class T> void outp(T a){cout<<'('<<a.fi<<','<<a.se<<')'<<'\n';}
template<class T> void outvp(T v){rep(i,v.size())cout<<'('<<v[i].fi<<','<<v[i].se<<')';cout<<'\n';}
template<class T> void outvvp(T v){rep(i,v.size())outvp(v[i]);}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<'\n';}
template<class T> void outvv(T v){rep(i,v.size())outv(v[i]);}
template<class T> bool isin(T x,T l,T r){return (l)<=(x)&&(x)<=(r);}
template<class T> void yesno(T b){if(b)out("yes");else out("no");}
template<class T> void YesNo(T b){if(b)out("Yes");else out("No");}
template<class T> void YESNO(T b){if(b)out("YES");else out("NO");}
template<class T> void noyes(T b){if(b)out("no");else out("yes");}
template<class T> void NoYes(T b){if(b)out("No");else out("Yes");}
template<class T> void NOYES(T b){if(b)out("NO");else out("YES");}
void outs(ll a,ll b){if(a>=inf-100)out(b);else out(a);}
ll gcd(ll a,ll b){if(b==0)return a;return gcd(b,a%b);}
ll modpow(ll a,ll b){a%=mod;if(b==0)return 1;if(b&1)return a*modpow(a,b-1)%mod;ll k=modpow(a,b/2);return k*k%mod;}
ll ma;
string s;
ll dp[305][305][305];
ll dfs(int i,int j,int k){
    if(i==j)return 1;
    if(i>j)return 0;
    if(dp[i][j][k]!=-1)return dp[i][j][k];
    if(s[i]==s[j])chmax(dp[i][j][k],dfs(i+1,j-1,k)+2);
    chmax(dp[i][j][k],dfs(i+1,j,k));
    chmax(dp[i][j][k],dfs(i,j-1,k));
    if(k!=ma)chmax(dp[i][j][k],dfs(i+1,j-1,k+1)+2);
    return dp[i][j][k];
}

int main(){
    cin>>s;
    ll n=s.size();cin>>ma;
    rep(i,n)rep(j,n)rep(t,ma+1)dp[i][j][t]=-1;
    out(dfs(0,n-1,0));
    //rep(i,n)rep(j,n)rep(t,ma+1)if(dp[i][j][t]!=-1)cout<<i<<' '<<j<<' '<<t<<' '<<dp[i][j][t]<<endl;
}
#include<bits/stdc++.h>
#define del(a,i) memset(a,i,sizeof(a))
#define ll long long
#define inl inline
#define il inl void
#define it inl int
#define ill inl ll
#define re register
#define ri re int
#define rl re ll
#define mid ((l+r)>>1)
#define lowbit(x) (x&(-x))
#define INF 0x3f3f3f3f
using namespace std;
template<class T>il read(T &x){
	int f=1;char k=getchar();x=0;
	for(;k>'9'||k<'0';k=getchar()) if(k=='-') f=-1;
	for(;k>='0'&&k<='9';k=getchar()) x=x*10+k-'0';
	x*=f;
}
template<class T>il _print(T x){
	if(x>=10) _print(x/10);
	putchar(x%10+'0');
}
template<class T>il print(T x){
	if(x<0) putchar('-'),x=-x;
	_print(x);
}
ll mul(ll a,ll b,ll mod){long double c=1.;return (a*b-(ll)(c*a*b/mod)*mod)%mod;}
it qpow(int x,int k,int mod){
	int res=1,bas=x;
	while(k){
		if(k&1) res=1ll*res*bas%mod;
		bas=1ll*bas*bas%mod,k>>=1;
	}
	return res;
}
const int N = 2e5+5,mod = 1e9+7;
it add(int x,int y){return x+y>=mod?x+y-mod:x+y;}
it mul(int x,int y){return 1ll*x*y%mod;}
il inc(int &x,int y){x=add(x,y);}
int n,m,k,ans,fac[N],ifac[N];
it C(int n,int m){return mul(mul(ifac[n-m],ifac[m]),fac[n]);}
int main(){
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	read(n),read(m),read(k),fac[0]=1;
	for(ri i=1;i<=n*m;++i) fac[i]=mul(fac[i-1],i);
	ifac[n*m]=qpow(fac[n*m],mod-2,mod);
	for(ri i=n*m-1;i>=0;--i) ifac[i]=mul(ifac[i+1],i+1);
	for(ri i=1;i<=n-1;++i) inc(ans,mul(mul(mul(m,m),n-i),i));
	for(ri i=1;i<=m-1;++i) inc(ans,mul(mul(mul(n,n),m-i),i));
	print(mul(ans,C(n*m-2,k-2)));
	return 0;
}