// In the name of Allah
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef complex<ld> cld;
#define all(x) (x).begin(),(x).end()
#define len(x) ((ll) (x).size())
#define F first
#define S second
#define pb push_back
#define sep ' '
#define endl '\n'
#define Mp make_pair
#define kill(x) cout << x << '\n', exit(0)
#define set_dec(x) cout << fixed << setprecision(x);
#define file_io(x,y) freopen(x, "r", stdin); freopen(y, "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = (1 << 20) + 4;
const ll oo = 1e18 + 4;
const ll inf = 1e12 + 4;
struct node {
ll lazy; pll sum;
ll valx; pll max;
};
int n, k; string s;
vector<ll> ls; pll dp[maxn];
node t[2 * maxn], null; set<int> st;
node f(node a, node b) {
node res; res.lazy = 0;
res.valx = a.valx + b.valx;
res.sum.F = a.sum.F + b.sum.F;
res.sum.S = a.sum.S + b.sum.S;
res.max = max(a.max, b.max);
return res;
}
void shift(int v, int tl, int tr) {
ll x = t[v].lazy; t[v].lazy = 0;
if (x == 0 || tr - tl == 1) return ;
for (int u : {2 * v + 1, 2 * v + 2}) {
t[u].lazy += x; t[u].max.F += x;
t[u].sum.F += t[u].valx * x;
}
}
void build(int v, int tl, int tr) {
t[v].lazy = 0;
if (tr - tl == 1) {
t[v] = null;
return ;
}
int mid = (tl + tr) / 2;
build(2 * v + 1, tl, mid); build(2 * v + 2, mid, tr);
t[v] = f(t[2 * v + 1], t[2 * v + 2]);
}
void set_val(int v, int tl, int tr, int i, pll x, int valx) {
shift(v, tl, tr);
if (tr - tl == 1) {
if (valx == 0) {
t[v] = null;
}
else {
t[v].sum = x; t[v].valx = valx;
if (x.F > 0) {
t[v].max = Mp(0, tl);
}
else {
ll R1 = -x.F;
if (R1 % valx != 0) {
t[v].max = Mp((R1 / valx) + 1, tl);
}
else {
t[v].max = Mp((R1 / valx) + (x.S < 0), tl);
}
}
t[v].max.F = (-t[v].max.F);
}
return ;
}
int mid = (tl + tr) / 2;
if (i < mid) set_val(2 * v + 1, tl, mid, i, x, valx);
else set_val(2 * v + 2, mid, tr, i, x, valx);
t[v] = f(t[2 * v + 1], t[2 * v + 2]);
}
void add_val(int v, int tl, int tr, int l, int r, ll x) {
l = max(l, tl); r = min(r, tr);
if (l >= tr || r <= tl) return ;
shift(v, tl, tr);
if (l == tl && r == tr) {
t[v].lazy += x; t[v].max.F += x;
t[v].sum.F += t[v].valx * x;
return ;
}
int mid = (tl + tr) / 2;
add_val(2 * v + 1, tl, mid, l, r, x); add_val(2 * v + 2, mid, tr, l, r, x);
t[v] = f(t[2 * v + 1], t[2 * v + 2]);
}
node get_res(int v, int tl, int tr, int l, int r) {
l = max(l, tl); r = min(r, tr);
if (l >= tr || r <= tl) return null;
shift(v, tl, tr);
if (l == tl && r == tr) return t[v];
int mid = (tl + tr) / 2;
return f(get_res(2 * v + 1, tl, mid, l, r), get_res(2 * v + 2, mid, tr, l, r));
}
void checkx() {
node res = get_res(0, 0, n + 1, 0, *st.rbegin());
while (res.max.F >= 0) {
int j = res.max.S; auto it = st.lower_bound(j);
if (it != st.begin()) {
it--; int r = (*it);
node res = get_res(0, 0, n + 1, r, j + 1);
set_val(0, 0, n + 1, r, res.sum, res.valx);
}
set_val(0, 0, n + 1, j, Mp(0, 0), 0); st.erase(j);
res = get_res(0, 0, n + 1, 0, *st.rbegin());
}
}
void updx(int i, ll valx) {
pll f = dp[i]; f.F += valx; f.S += 1;
if (len(st) > 0) {
int j = (*st.rbegin());
node res = get_res(0, 0, n + 1, j, j + 1);
pll g = res.sum; g.F -= f.F; g.S -= f.S;
set_val(0, 0, n + 1, j, g, res.valx);
}
set_val(0, 0, n + 1, i, f, 1); st.insert(i);
checkx();
}
void addx(int x) {
auto it = st.lower_bound(x);
if (it == st.begin()) return ;
it--; int j = (*it);
add_val(0, 0, n + 1, 0, j, 1);
node res = get_res(0, 0, n + 1, j, j + 1);
auto g = res.sum; g.F += (x - j);
set_val(0, 0, n + 1, j, g, res.valx);
checkx();
}
void cal(ll valx) {
build(0, 0, n + 1); st.clear();
dp[0] = Mp(0, 0); updx(0, valx);
for (int i = 1; i <= n; i++) {
addx(ls[i - 1]); int j = (*st.begin());
dp[i] = get_res(0, 0, n + 1, j, n + 1).sum; updx(i, valx);
}
}
void solve() {
cin >> n >> k >> s;
ll res = 0; int x = 0;
for (int i = 0; i < (2 * n); i++) {
if (s[i] == 'B') x++;
else ls.pb(x);
}
for (int i = 0; i < n; i++) {
if (ls[i] > i) {
res += (ls[i] - i); ls[i] = i;
}
}
ll l = -1, r = inf;
while (r - l > 1) {
ll mid = (l + r) / 2; cal(mid);
if (dp[n].S > k) l = mid;
else r = mid;
}
cal(r);
cout << res + (dp[n].F - (k * r)) << endl;
}
int main() {
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
null.lazy = 0; null.valx = 0;
null.sum = Mp(0, 0); null.max = Mp(-oo, -1);
int T = 1;
while (T--) {
solve();
}
return 0;
}
