#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=200005;
int n,k;char s[N];
struct node{
	int len,slink;
	int trans[26];
}st[N];
int sz,lst;
int deg[N],mn[N],mx[N];queue<int> Q;ll w[N],d1[N],d2[N];
void init(){
	for(int i=sz;i>=0;i--){
		st[i].len=st[i].slink=mx[i]=0;mn[i]=1e9;
		for(int j=0;j<26;j++)st[i].trans[j]=0;
	}
	st[0].len=0;st[0].slink=-1;sz=lst=0;
}
void add(int ch){
	int cur=++sz;st[cur].len=st[lst].len+1;mx[cur]=mn[cur]=ch;
	int p=lst;lst=cur;int c=s[ch]-'a';
	while(p!=-1&&!st[p].trans[c])st[p].trans[c]=cur,p=st[p].slink;
	if(p==-1){st[cur].slink=0;return;}
	int q=st[p].trans[c];if(st[p].len+1==st[q].len){st[cur].slink=q;return;}
	int r=++sz;st[r].len=st[p].len+1;st[r].slink=st[q].slink;
	for(int i=0;i<26;i++)st[r].trans[i]=st[q].trans[i];
	while(p!=-1&&st[p].trans[c]==q)st[p].trans[c]=r,p=st[p].slink;
	st[q].slink=st[cur].slink=r;
}
ll query(int l,int r){
	init();for(int i=l;i<=r;i++)add(i);
	for(int i=1;i<=sz;i++)++deg[st[i].slink];
	for(int i=1;i<=sz;i++)if(!deg[i])Q.push(i);
	while(!Q.empty()){
		int u=Q.front(),v=st[u].slink;Q.pop();
		mn[v]=min(mn[v],mn[u]);mx[v]=max(mx[v],mx[u]);
		--deg[v];if(!deg[v])Q.push(v);
	}
	for(int i=1;i<=sz;i++){
		int p=st[i].len,q=st[st[i].slink].len+1,x=mn[i],y=mx[i];
		if(y-x+1<=q);
		else if(y-x+1<=p)d2[x]+=y-q-x+1,d2[x+1]-=y-q-x+1,d2[x+1]--,d2[y-q+2]++;
		else d2[x]+=p-q+1,d2[x+1]-=p-q+1,d2[y-p+1]--,d2[y-q+2]++;
	}
	for(int i=l;i<=r;i++)d1[i]=d1[i-1]+d2[i],w[i]=w[i-1]+d1[i];
	ll res=0;for(int i=l;i<=r;i++)res+=w[i]*w[i];
	for(int i=l-1;i<=r+1;i++)d1[i]=d2[i]=w[i]=0;
	return res;
}
inline bool check(ll x){
	int cnt=0;
	for(int i=1;i<=n;){
		++cnt;int j=0;
		for(;i+(1<<j)-1<=n;j++)
			if(query(i,i+(1<<j)-1)>x)break;
		--j;int i1=i+(1<<j);--j;
		for(;j>=0;j--)if(i1+(1<<j)-1<=n)
			if(query(i,i1+(1<<j)-1)<=x)i1+=(1<<j);
		i=i1;
	}
	return cnt<=k;
}
int main(){
//	freopen("word.in","r",stdin);
//	freopen("word.out","w",stdout);
	scanf("%d%d",&n,&k);
	scanf("%s",s+1);
	ll L=0,R=1e18,ans=1e18;
	while(L<=R){
		ll mid=L+R>>1;
		if(check(mid))R=mid-1,ans=mid;
		else L=mid+1;
	}
	printf("%lld\n",ans);
	return 0;
}