#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>
constexpr int N(5e4+10),iinf(1e9);
using ll=long long;
constexpr ll inf(2e18);
namespace T
{
	int mxlen[N<<1],link[N<<1],trans[N<<1][26],sz,lst,n,pos[N<<1],mx[N<<1],mn[N<<1],mnlen[N<<1];
	std::vector<int> es[N<<1];
	void init()
	{
		std::memset(pos+1,0,sizeof(int)*sz);
		std::memset(mxlen+1,0,sizeof(int)*sz);
		std::memset(link+1,0,sizeof(int)*sz);
		std::memset(trans+1,0,sizeof(trans[0])*sz);
		sz=lst=1;n=0;
	}
	void extend(int id)
	{
		int cur(++sz);pos[cur]=++n;int p(lst);mxlen[cur]=mxlen[lst]+1;
		for(;p && !trans[p][id];p=link[p]) trans[p][id]=cur;
		if(!p) link[cur]=1;
		else
		{
			int q(trans[p][id]);
			if(mxlen[q]==mxlen[p]+1) link[cur]=q;
			else
			{
				int c(++sz);mxlen[c]=mxlen[p]+1;
				std::memcpy(trans[c],trans[q],sizeof(trans[0]));
				for(;p && trans[p][id]==q;p=link[p]) trans[p][id]=c;
				link[c]=link[q];link[q]=link[cur]=c;
			}
		}
		lst=cur;
	}
	void dfs(int u)
	{
		if(pos[u]) mn[u]=mx[u]=pos[u];
		else mn[u]=iinf,mx[u]=0;
		for(int v:es[u]) dfs(v),mn[u]=std::min(mn[u],mn[v]),mx[u]=std::max(mx[u],mx[v]);
	}
	ll calc()
	{
		for(int i(1);i<=sz;++i) es[i].clear();
		for(int i(2);i<=sz;++i) es[link[i]].emplace_back(i),mnlen[i]=mxlen[link[i]]+1;
		dfs(1);
		static int b[N];
		for(int i(1);i<=n+1;++i) b[i]=0;
		for(int i(2);i<=sz;++i)
		{
			int l(mnlen[i]),r(mxlen[i]),j(mn[i]),k(mx[i]);
			if(k-j<l) continue;r=std::min(r,k-j);
			b[j]+=r-l+1;b[j+1]-=(r-l+1);b[k-r+1]-=1;b[k-l+2]+=1;
		}
		ll ans(0),cur(0),d(0);
		for(int i(1);i<n;++i)
		{
			d+=b[i];
			cur+=d;
			ans+=cur*cur;
			ans=std::min(ans,inf);
		}
		return ans;
	}
}
ll calc(char *s,int l,int r)
{
	T::init();
	for(int i(l);i<=r;++i) T::extend(s[i]-'a');
	return T::calc();
}
bool check(ll mid,int k,char *s,int n)
{
	int c(0);
	for(int l(1),r;l<=n;l=r+1)
	{
		++c;if(c>k) return false;
		int j;
		for(j=1;l+(1<<j)-1<=n;++j)
		{
			if(calc(s,l,l+(1<<j)-1)>mid) break;
		}
		--j;r=l+(1<<j)-1;
		for(int t(j-1);t>=0;--t) if(r+(1<<t)<=n && calc(s,l,r+(1<<t))<=mid)
		{
			r+=(1<<t);
		}
	}
	return true;
}
int main()
{
	static char s[N];int n,k;
	std::ios::sync_with_stdio(false);std::cin.tie(nullptr);
	std::cin>>n>>k>>(s+1);
	ll l(0),r(1e18),mid,ans;
	while(l<=r)
	{
		mid=(l+r)>>1;
		if(check(mid,k,s,n)) r=mid-1,ans=mid;
		else l=mid+1;
	}
	std::cout<<ans<<std::endl;
	return 0;
}