#include<bits/stdc++.h>
using namespace std;
// define
#define execute cerr << " Time: " << fixed << setprecision(6) << (1.0 * clock() / CLOCKS_PER_SEC) << "s\n";
#define ll long long
#define ii pair <int , int>
#define iii pair <int , ii>
#define se second
#define fi first
#define all(v) (v).begin() , (v).end()
#define Unique(v) sort(all(v)) , v.resize(unique(all(v)) - v.begin())
#define bit(x,i) (((x) >> (i)) & 1LL)
#define flip(x,i) ((x) ^ (1LL << (i)))
#define ms(d,x) memset(d , x , sizeof(d))
#define exist __exist
#define ends __ends
#define visit visited
#define left __left
#define right __right
#define prev __prev
#define next __next
#define sitingfake 1
#define orz 1
//constant
const long long mod = 1e9 + 7;
const long long linf = 4557430888798830399LL;
const long long nlinf = -4485090715960753727LL;
const int LOG = 20;
const int inf = 1061109567;
const int ninf = -1044266559;
const int dx[] = {0 , -1 , 0 , 1};
const int dy[] = {-1 , 0 , 1 , 0};
template<typename T> bool maximize(T &a, const T &b)
{
if(a < b) {a = b; return 1;}
return 0;
}
template<typename T> bool minimize(T &a, const T &b)
{
if(a > b) {a = b; return 1;}
return 0;
}
void Plus(ll & a ,ll b)
{
b %= mod;
a += b;
if(a < 0) a += mod;
a %= mod;
return;
}
void Mul(ll & a, ll b)
{
(a *= (b % mod)) %= mod;
return;
}
//code
const int maxn = 1e6 + 7;
string s;
int n , k;
int a[maxn] , b[maxn] , pref[maxn] , timerA , timerB;
namespace sub3
{
int dp[2][5005];
int cost[5005][5005];
void compute()
{
for(int l = 1; l <= n; l++)
{
for(int r = l; r <= n; r++)
{
if(a[r] > b[l])
{
cost[l][r] = cost[l][r - 1] + pref[a[r]] - pref[b[l] - 1];
}
else cost[l][r] = cost[l][r - 1];
}
}
}
void DnC(int l , int r, int optl , int optr , int cur)
{
if(l > r) return;
int mid = (r + l) >> 1;
int optk;
dp[cur][mid] = inf;
for(int i = optl; i <= min(mid , optr); i++)
{
if(minimize(dp[cur][mid] , dp[!cur][i - 1] + cost[i][mid]))
{
optk = i;
}
}
DnC(l , mid - 1 , optl , optk , cur);
DnC(mid + 1 , r , optk , optr , cur);
}
void solve()
{
ms(dp , 0x3f);
dp[0][0] = 0;
compute();
for(int i = 1; i <= n; i++)
{
dp[1][i] = cost[1][i];
}
for(int i = 2; i <= k; i++)
{
DnC(i , n , 1 , n , i & 1);
}
cout << dp[k & 1][n];
}
}
namespace sub5
{
ll cnt[2 * maxn];
ll sumpref[2 * maxn];
int pos[maxn];
pair <ll , int> dp[maxn];
struct CHT {
struct Line {
ll a; // slope
ll b; // intercept
int seg; // segments
// evaluate (use __int128 to avoid overflow)
pair<ll,int> eval(ll x) const {
__int128 v = (__int128)a * (__int128)x + (__int128)b;
return { (ll)v, seg };
}
};
deque<Line> dq;
// check if l2 is unnecessary between l1 and l3
static bool is_bad(const Line &l1, const Line &l2, const Line &l3) {
// intersection(l1,l2) >= intersection(l2,l3) => l2 is bad
// (b2 - b1)/(a1 - a2) >= (b3 - b2)/(a2 - a3)
// cross-multiply to avoid doubles:
__int128 left = (__int128)(l2.b - l1.b) * (__int128)(l2.a - l3.a);
__int128 right = (__int128)(l3.b - l2.b) * (__int128)(l1.a - l2.a);
return left >= right;
}
// add line, slopes must be strictly decreasing (new.a < last.a)
void add(Line L) {
while (dq.size() >= 2 && is_bad(dq[dq.size()-2], dq[dq.size()-1], L))
dq.pop_back();
dq.push_back(L);
}
// query min at x, queries must be non-decreasing
pair<ll,int> query(ll x) {
// while front is worse than next at x, pop front
while (dq.size() >= 2 && dq[0].eval(x) >= dq[1].eval(x)) dq.pop_front();
return dq.front().eval(x);
}
bool empty() const { return dq.empty(); }
void clear() { dq.clear(); }
};
ll cost(int l , int r)
{
if(a[r] < b[l]) return 0;
return -pref[b[l] - 1] * (cnt[a[r]] - cnt[pos[l] - 1]) + sumpref[a[r]] - sumpref[pos[l] - 1];
}
pair <ll , int> compute(ll lambda)
{
dp[0] = {0 , 0};
int it = 1;
multiset <pair <ll ,int>> Min;
Min.insert(dp[0]);
CHT cht;
for(int i = 1; i <= n; i++)
{
dp[i] = {linf , inf};
while(it <= i && b[it] <= a[i])
{
cht.add({-pref[b[it] - 1] , pref[b[it] - 1] * cnt[pos[it] - 1] - sumpref[pos[it] - 1] + dp[it - 1].fi , dp[it - 1].se });
//cht.flag = 1;
Min.erase(Min.find(dp[it - 1]));
it++;
}
dp[i] = {linf , inf};
if(!cht.empty())
{
pair <ll , int> val = cht.query(cnt[a[i]]);
val.fi += lambda + sumpref[a[i]];
val.se++;
minimize(dp[i] , val);
}
if(!Min.empty())
{
pair <ll , int> val = *Min.begin();
val.fi += lambda;
val.se++;
minimize(dp[i] , val);
}
Min.insert(dp[i]);
}
return dp[n];
}
void solve()
{
for(int i = 1; i <= 2 * n; i++)
{
if(s[i - 1] == 'A')
{
sumpref[i] = pref[i];
cnt[i] = 1;
}
sumpref[i] += sumpref[i - 1];
cnt[i] += cnt[i - 1];
}
for(int i = 1; i <= n; i++)
{
pos[i] = max(a[i] , b[i]);
}
ll left = 0 , right = 1e12 , ans = 0;
while(left <= right)
{
ll mid = (left + right) >> 1;
if(compute(mid).se <= k)
{
ans = mid;
right = mid - 1;
}
else left = mid + 1;
}
pair <ll , int> tmp = compute(ans);
cout << tmp.fi - 1ll * ans * tmp.se;
}
}
void solve(void)
{
cin >> n >> k;
cin >> s;
for(int i = 1; i <= 2 * n; i++)
{
pref[i] = pref[i - 1];
if(s[i - 1] == 'A')
{
a[i] = 0;
a[++timerA] = i;
}
else
{
a[i] = 1;
pref[i] += 1;
b[++timerB] = i;
}
}
sub5 :: solve();
}
/**
5 3
AABABABBAB
**/
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#define task ""
if(fopen(task".inp","r"))
{
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
int tc = 1;
// cin >> tc;
while(tc--) solve();
// execute;
}
