Array Splitting

#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <array>
#include <stack>
#include <queue>
#include <random>
#include <numeric>
#include <functional>
#include <chrono>
#include <utility>
#include <iomanip>
#include <assert.h>

using namespace std;

void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)

#define rng_init mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define rng_seed(x) mt19937 rng(x)
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define int long long

const int MXN = 3e5 + 5, INF = 1e18;
int N, K;
int A[MXN];

pair<int, int> check(int penalty) {
    vector<int> dp(N + 1, INF), subarrays(N + 1);
    dp[0] = subarrays[0] = 0;

    pair<int, int> mn = {-A[1], 0};

    for (int i = 1; i <= N; i++) {
        if (dp[i - 1] - A[i] <= mn.first)
            mn = make_pair(dp[i - 1] - A[i], subarrays[i - 1]);

        dp[i] = A[i] + mn.first + penalty;
        subarrays[i] = mn.second + 1;
    }

    return make_pair(dp[N] - penalty * subarrays[N], subarrays[N]);
}

void solve() {
    cin >> N >> K;

    for (int i = 1; i <= N; i++)
        cin >> A[i];

    int low = -INF, high = INF;
    while (low <= high) {
        int mid = low + (high - low) / 2;

        auto [val, subarrays] = check(mid);
        dbg(mid, val, subarrays);

        if (subarrays < K) high = mid - 1;
        else if (subarrays > K) low = mid + 1;
        else {
            cout << val;
            return;
        }
    }
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int TC = 1;
    // cin >> TC;
    while (TC--) solve();
}