# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll INF=2e18;
int n,k,a[100010],minn[100010],maxn[100010],buc[50010],trans[100010][26],len[100010],lnk[100010],tot;
ll f0[50010],f1[50010];
char s[50010];
void upd(int l,int r,int k,int b){f0[l]+=b;f0[r+1]-=b;f1[l]+=k;f1[r+1]-=k;}
ll mul(ll a,ll b)
{
	if(!a || !b) return 0;
	return a<=INF/b?a*b:INF;
}
ll sq(ll a){return mul(a,a);}
ll add(ll a,ll b){return min(a+b,INF);}
int insert(int c,int lst)
{
	int cur=++tot,p=lst;
	len[cur]=len[p]+1;
	memset(trans[cur],0,sizeof(int)*26);
	for(;p && !trans[p][c];p=lnk[p]) trans[p][c]=cur;
	if(!p) lnk[cur]=1;
	else
	{
		int q=trans[p][c];
		if(len[q]==len[p]+1) lnk[cur]=q;
		else
		{
			int t=++tot;maxn[t]=0;minn[t]=1e9;
			len[t]=len[p]+1;lnk[t]=lnk[q];
			lnk[q]=lnk[cur]=t;
			memcpy(trans[t],trans[q],sizeof(int)*26);
			for(;p && trans[p][c]==q;p=lnk[p]) trans[p][c]=t;
		}
	}
	return cur;
}
ll calc(int l,int r)
{
	tot=1;memset(trans[1],0,sizeof(int)*26);
	int lst=1;
	for(int i=l;i<=r;i++)
	{
		lst=insert(s[i]-'a',lst);
		maxn[lst]=minn[lst]=i;
	}
	memset(buc+1,0,sizeof(int)*(r-l+1));
	for(int i=1;i<=tot;i++) buc[len[i]]++;
	for(int i=1;i<=r-l+1;i++) buc[i]+=buc[i-1];
	for(int i=tot;i>=1;i--) a[buc[len[i]]--]=i;
	for(int i=tot;i>1;i--)
	{
		int u=a[i];
		maxn[lnk[u]]=max(maxn[lnk[u]],maxn[u]);
		minn[lnk[u]]=min(minn[lnk[u]],minn[u]);
	}
	memset(f0+l,0,sizeof(ll)*(r-l+1));
	memset(f1+l,0,sizeof(ll)*(r-l+1));
	for(int i=2;i<=tot;i++)
	{
		if(maxn[i]-len[i]+1>minn[i]) upd(minn[i]+1,maxn[i]-len[i]+1,0,len[i]-len[lnk[i]]);
		int l=max(maxn[i]-len[i]+2,minn[i]+1),r=maxn[i]-len[lnk[i]];
		if(l<=r) upd(l,r,-1,maxn[i]-len[lnk[i]]+1);
	}
	for(int i=l+1;i<=r;i++) f0[i]+=f0[i-1],f1[i]+=f1[i-1];
	ll ans=0;
	for(int i=l+1;i<=r;i++) ans=add(ans,sq(f1[i]*i+f0[i]));
	return ans;
}
bool judge(ll lim)
{
	int cnt=0,cur=1;
	while(cur<=n)
	{
		cnt++;
		if(cnt>k) return false;
		auto chk=[&](int l){return cur+l-1<=n && calc(cur,cur+l-1)<=lim;};
		int p=0,len=0;
		while(chk(1<<(p+1))) p++;
		len=1<<p;
		for(int i=p-1;i>=0;i--)
			if(chk(len+(1<<i))) len+=1<<i;
		cur+=len;
	}
	return true;
}
int main()
{
	cin>>n>>k;
	scanf("%s",s+1);
	ll l=0,r=1e18,mid;
	while(l<r)
	{
		mid=(l+r)/2;
		if(judge(mid)) r=mid;
		else l=mid+1;
	}
	cout<<l<<endl;
	return 0;
}