Problem: You are given array a_1, a_2, ..., a_n. You need to split it into k subsegments (so every element is included in exactly one subsegment).

The weight of a subsegment a_l, a_{l+1}, ..., a_r is equal to (r - l + 1) ⋅ max_{l ≤ i ≤ r}(a_i). The weight of a partition is a total weight of all its segments.

Find the partition of minimal weight.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^4, 1 ≤ k ≤ min(100, n)) — the length of the array a and the number of subsegments in the partition.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^4) — the array a.

Output

Print single integer — the minimal weight among all possible partitions.

Examples

Input


4 2
6 1 7 4


Output


25


Input


4 3
6 1 7 4


Output


21


Input


5 4
5 1 5 1 5


Output


21

Note

The optimal partition in the first example is next: 6 1 7 \bigg| 4.

The optimal partition in the second example is next: 6 \bigg| 1 \bigg| 7 4.

One of the optimal partitions in the third example is next: 5 \bigg| 1 5 \bigg| 1 \bigg| 5.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
const int MAXN = 20005;
using pi = pair<lint, lint>;
int n, k;
int dp[MAXN], nxt[MAXN], a[MAXN];
using line_t = double;
const line_t is_query = -1e18;
struct Line {
  line_t m, b;
  mutable function<const Line*()> succ;
  bool operator<(const Line& rhs) const {
    if (rhs.b != is_query) return m < rhs.m;
    const Line* s = succ();
    if (!s) return 0;
    line_t x = rhs.m;
    return b - s->b < (s->m - m) * x;
  }
};
struct HullDynamic : public multiset<Line> {
  bool bad(iterator y) {
    auto z = next(y);
    if (y == begin()) {
      if (z == end()) return 0;
      return y->m == z->m && y->b <= z->b;
    }
    auto x = prev(y);
    if (z == end()) return y->m == x->m && y->b <= x->b;
    return (x->b - y->b) * (z->m - y->m) >= (y->b - z->b) * (y->m - x->m);
  }
  void insert_line(line_t m, line_t b) {
    m = -m, b = -b;
    auto y = insert({m, b});
    y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
    if (bad(y)) {
      erase(y);
      return;
    }
    while (next(y) != end() && bad(next(y))) erase(next(y));
    while (y != begin() && bad(prev(y))) erase(prev(y));
  }
  line_t query(line_t x) {
    if (empty()) return 1e9;
    auto l = *lower_bound((Line){x, is_query});
    return -(int)round(l.m * x + l.b);
  }
} H;
struct foo {
  int curMax, dpv, idx;
};
struct cht {
  deque<pi> v;
  void clear() { v.clear(); }
  bool bad(pi x, pi y, pi z) {
    auto v1 = (long double)(y.second - x.second) / (x.first - y.first);
    auto v2 = (long double)(z.second - y.second) / (y.first - z.first);
    return v1 > v2;
  }
  void add(lint x, lint y) {
    if (v.size() && v.back().first == x) {
      y = min(y, v.back().second);
      v.pop_back();
    }
    while (v.size() >= 2 && bad(v[v.size() - 2], v.back(), pi(x, y))) {
      v.pop_back();
    }
    v.emplace_back(x, y);
  }
  int query(int x) {
    if (v.empty()) return 1e9;
    lint ret = 1e9;
    for (auto& i : v) ret = min(ret, i.first * x + i.second);
    return ret;
    int s = 0, e = v.size() - 1;
    while (s != e) {
      int m = (s + e) / 2;
      if (v[m].first * x + v[m].second > v[m + 1].first * x + v[m + 1].second)
        s = m + 1;
      else
        e = m;
    }
    return v[s].first * x + v[s].second;
  }
  int yreuq(int x) { return query(x); }
} cht;
int tab[MAXN];
void dnc(int s, int e) {
  if (s == e) return;
  int m = (s + e) / 2;
  dnc(s, m);
  dnc(m + 1, e);
  int curMax = 0;
  vector<foo> v;
  for (int i = m; i >= s; i--) {
    if (dp[i] < 1e9) v.push_back({curMax, dp[i], i});
    curMax = max(curMax, a[i]);
  }
  tab[m] = 0;
  for (int i = m + 1; i <= e; i++) {
    tab[i] = max(tab[i - 1], a[i]);
  }
  H.clear();
  int ptr = v.size();
  for (int i = e; i > m; i--) {
    while (ptr > 0 && v[ptr - 1].curMax >= tab[i]) {
      auto j = v[--ptr];
      H.insert_line(j.curMax, j.dpv - j.idx * j.curMax);
    }
    nxt[i] = min(nxt[i], (int)H.query(i));
  }
  H.clear();
  ptr = 0;
  for (int i = m + 1; i <= e; i++) {
    while (ptr < v.size() && v[ptr].curMax < tab[i]) {
      H.insert_line(-v[ptr].idx, v[ptr].dpv);
      ptr++;
    }
    nxt[i] = min(nxt[i], (int)H.query(tab[i]) + i * tab[i]);
  }
}
void solve() { dnc(0, n); }
int main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  memset(dp, 0x3f, sizeof(dp));
  dp[0] = 0;
  for (int i = 1; i <= k; i++) {
    memset(nxt, 0x3f, sizeof(nxt));
    solve();
    memcpy(dp, nxt, sizeof(dp));
  }
  cout << dp[n] << endl;
}