#define local
#ifndef local
#include ""
#endif
#include <bits/stdc++.h>
// using namespace __gnu_pbds;
using namespace std;
#define int long long
#define fi first
#define se second
#define pb push_back
#define mp make_pair
typedef pair<int, int> ii;
typedef pair<ii, int> iii;
typedef pair<ii, ii> iiii;
const int N = 3e5 + 5;
const int oo = 1e18 + 7, mod = 1e9 + 7;
mt19937 rng(1);
int rnd(int l, int r)
{
int temp = rng() % (r - l + 1);
return abs(temp) + l;
}
int n, k, a[N];
vector<vector<int>> cal(int l, int r)
{ // from left to right: (0,0), (0,1), (1,0), (1,1)
if (l == r)
{
vector<vector<int>> v;
v.pb({0, -oo});
v.pb({-oo, -oo});
v.pb({-oo, -oo});
v.pb({-oo, a[l]});
return v;
}
int mid = (l + r) >> 1;
vector<vector<int>> cal1 = cal(l, mid), cal2 = cal(mid + 1, r);
vector<vector<int>> ans;
for (int i = 0; i <= 3; i++)
{
vector<int> temp;
temp.resize(r - l + 2);
for (int j = 0; j < temp.size(); j++)
temp[j] = -oo;
ans.pb(temp);
}
int left_len = (mid - l + 1), right_len = (r - mid);
// cout << "START " << l << " " << r << "\n";
// int want = (l + r + 1) >> 1;
for (int le = 0; le < 2; le++)
{
for (int ri = 0; ri < 2; ri++)
{
for (int mile = 0; mile < 2; mile++)
{
for (int miri = 0; miri < 2; miri++)
{
int er = mile & miri;
int cur_opt = 0;
int temp1 = ((left_len + 1 - !(le & mile)) / 2), temp2 = (right_len + 1 - !(ri & miri)) / 2;
// cout << le << " " << ri << " " << mile << " " << miri << " " << temp1 << " " << temp2 << "\n";
for (int tol = 0; tol <= temp1 + temp2 - er; tol++)
{
while (tol - cur_opt + er > temp2)
cur_opt++;
while (cur_opt < min(temp1, tol + er))
{
// cout << cur_opt << "\n";
int val1 = cal1[(le << 1) | mile][cur_opt] + cal2[(miri << 1) | ri][tol - cur_opt + er];
int val2 = cal1[(le << 1) | mile][cur_opt + 1] + cal2[(miri << 1) | ri][tol - cur_opt - 1 + er];
// cout << val1 << " " << val2 << "\n";
if (val1 < val2)
cur_opt++;
else
break;
}
// cout << le << " " << ri << " " << mile << " " << miri << " " << tol << " " << cur_opt << " " << tol - cur_opt + er << " " << cal1[(le << 1) | mile][cur_opt] + cal2[(miri << 1) | ri][tol - cur_opt + er] << "\n";
ans[(le << 1) | ri][tol] = max(ans[(le << 1) | ri][tol], cal1[(le << 1) | mile][cur_opt] + cal2[(miri << 1) | ri][tol - cur_opt + er]);
}
}
}
}
}
// cout << l << " " << r << "\n";
for (int i = 0; i < 4; i++)
{
// cout << "OK ";
// for (int j = 0; j < ans[i].size(); j++)
// cout << ans[i][j] << " ";
// cout << "\n";
}
return ans;
}
#ifdef local
void process()
{
cin >> n >> k;
for (int i = 1; i <= n; i++)
cin >> a[i];
vector<vector<int>> v = cal(1, n);
int answer = -oo;
for (int i = 0; i <= k; i++)
answer = max(answer, max({v[0][i], v[1][i], v[2][i], v[3][i]}));
cout << answer << "\n";
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
// freopen("temp.inp", "r", stdin);
// freopen("temp.out", "w", stdout);
process();
}
#endif
