Problem: Misha has an array of integers of length n. He wants to choose k different continuous subarrays, so that each element of the array belongs to at least one of the chosen subarrays.

Misha wants to choose the subarrays in such a way that if he calculated the sum of elements for each subarray, and then add up all these sums, the resulting value was maximum possible.

Input

The first line of input contains two integers: n, k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ n·(n + 1) / 2) — the number of elements in the array and the number of different subarrays that must be chosen.

The second line contains n integers ai ( - 50 000 ≤ ai ≤ 50 000) — the elements of the array.

Output

Output one integer — the maximum possible value Misha can get by choosing k different subarrays.

Example

Input

5 4
6 -4 -10 -4 7


Output

11

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using ll = long long;
const int N = 100000 + 10;
const ll inf = 8333583335000000000ll;
int a[N], cov[N], sum_rank[N], n;
ll sum[N], max_sum[N], min_sum[N];
ll m;
struct SegmentTree {
  struct node {
    ll mi, mx;
  } data[N << 2];
  node merge(const node &a, const node &b) {
    node c;
    c.mi = std::min(a.mi, b.mi);
    c.mx = std::max(a.mx, b.mx);
    return c;
  }
  void build(int rt, int l, int r) {
    if (l + 1 == r) {
      data[rt].mx = data[rt].mi = sum[l];
      return;
    }
    int m = (l + r) >> 1;
    build(rt << 1, l, m);
    build(rt << 1 | 1, m, r);
    data[rt] = merge(data[rt << 1], data[rt << 1 | 1]);
  }
  node ask(int rt, int l, int r, int L, int R) {
    if (L <= l && R >= r) return data[rt];
    int m = (l + r) >> 1;
    node ret{inf, -inf};
    if (L < m) ret = merge(ret, ask(rt << 1, l, m, L, R));
    if (R > m) ret = merge(ret, ask(rt << 1 | 1, m, r, L, R));
    return ret;
  }
} st;
ll get(int l, int r) {
  auto res = st.ask(1, 0, n, l + 1, r + 1);
  return res.mi - res.mx;
}
namespace treap {
struct node {
  int sz, i, mx;
  ll val, sum;
  node *l, *r;
  node() = default;
  node(int i, ll v) : sz(1), i(i), mx(i), val(v), sum(v), l(0), r(0) {}
  node *update() {
    sz = 1, mx = i, sum = val;
    if (l) sz += l->sz, mx = std::max(mx, l->mx), sum += l->sum;
    if (r) sz += r->sz, mx = std::max(mx, r->mx), sum += r->sum;
    return this;
  }
} pool[N], *p, *rt;
node *new_node(int i, ll v) {
  *p = node(i, v);
  return p++;
}
void init() {
  p = pool;
  rt = new_node(n, 0);
}
bool random(int a, int b) { return rand() % (a + b) < a; }
node *merge(node *l, node *r) {
  if (!l || !r) return l ? l : r;
  if (random(l->sz, r->sz)) {
    l->r = merge(l->r, r);
    return l->update();
  } else {
    r->l = merge(l, r->l);
    return r->update();
  }
}
std::pair<node *, node *> split(node *o, ll v) {
  node *l = 0, *r = 0;
  if (!o) return {l, r};
  if (o->val <= v) {
    std::tie(o->r, r) = split(o->r, v);
    l = o;
  } else {
    std::tie(l, o->l) = split(o->l, v);
    r = o;
  }
  o->update();
  return {l, r};
}
std::pair<node *, node *> split_by_size(node *o, int sz) {
  node *l = 0, *r = 0;
  if (!o) return {l, r};
  int ls = o->l ? o->l->sz : 0;
  if (ls + 1 <= sz) {
    std::tie(o->r, r) = split_by_size(o->r, sz - ls - 1);
    l = o;
  } else {
    std::tie(l, o->l) = split_by_size(o->l, sz);
    r = o;
  }
  o->update();
  return {l, r};
}
int rank(ll v) {
  node *a, *b;
  std::tie(a, b) = split(rt, v);
  int ret = a ? a->sz : 0;
  rt = merge(a, b);
  return ret;
}
void add(int i, ll v) {
  node *a, *b, *p = new_node(i, v);
  std::tie(a, b) = split(rt, v);
  rt = merge(a, merge(p, b));
}
}  // namespace treap
namespace kth {
std::multiset<ll> A, B;
ll sum;
int k;
void init(int _k) {
  k = _k;
  sum = 0;
}
void fix() {
  while (A.size() > k) {
    ll u = *A.rbegin();
    A.erase(A.find(u));
    B.insert(u);
    sum -= u;
  }
  while (A.size() < k && B.size()) {
    ll u = *B.begin();
    B.erase(B.find(u));
    A.insert(u);
    sum += u;
  }
}
void add(ll v) {
  A.insert(v);
  sum += v;
  fix();
}
void del(ll v) {
  if (B.find(v) != B.end())
    B.erase(B.find(v));
  else
    A.erase(A.find(v)), sum -= v;
  fix();
}
void reduce() {
  --k;
  fix();
}
}  // namespace kth
std::vector<ll> xs;
namespace fen {
int bit[N];
void init() {
  for (int i = 0; i < xs.size(); ++i) bit[i] = 0;
}
void add(int x, int v) {
  for (; x < xs.size(); x += ~x & x + 1) bit[x] += v;
}
int get(int x, int r = 0) {
  for (; x >= 0; x -= ~x & x + 1) r += bit[x];
  return r;
}
}  // namespace fen
ll count_ge(ll bound) {
  fen::init();
  fen::add(sum_rank[n], 1);
  ll ret = 0;
  for (int i = n - 1; i >= 0; --i) {
    int v =
        std::upper_bound(xs.begin(), xs.end(), sum[i] - bound) - xs.begin() - 1;
    ret += fen::get(v);
    fen::add(sum_rank[i], 1);
  }
  return ret;
}
ll find_border_sum(ll m) {
  ll delta = -5000000000ll - 1;
  ll left = 0, right = 100000000000ll;
  while (left < right) {
    ll mid = (left + right + 1) >> 1;
    if (count_ge(mid + delta) >= m)
      left = mid;
    else
      right = mid - 1;
  }
  return delta + left;
}
void trans(treap::node *o, std::vector<std::pair<int, int>> &pt, int upp,
           int l) {
  if (pt.size() == upp) return;
  if (!o) return;
  pt.emplace_back(l, o->i - 1);
  trans(o->l, pt, upp, l);
  trans(o->r, pt, upp, l);
}
int main() {
  scanf("%d%lld", &n, &m);
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
  }
  sum[n] = min_sum[n] = 0;
  for (int i = n - 1; i >= 0; --i) {
    sum[i] = sum[i + 1] + a[i];
    min_sum[i] = std::min(min_sum[i + 1], sum[i]);
    cov[i] = -1;
  }
  max_sum[0] = sum[0];
  for (int i = 1; i <= n; ++i) {
    max_sum[i] = std::max(max_sum[i - 1], sum[i]);
  }
  xs.assign(n + 1, 0);
  for (int i = 0; i <= n; ++i) xs[i] = sum[i];
  std::sort(xs.begin(), xs.end());
  xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
  for (int i = 0; i <= n; ++i) {
    sum_rank[i] = std::lower_bound(xs.begin(), xs.end(), sum[i]) - xs.begin();
  }
  st.build(1, 0, n);
  ll p = std::max<ll>(m - n, 0);
  ll q = m - p;
  ll sum1 = find_border_sum(p);
  ll sum2 = find_border_sum(m);
  ll pp = count_ge(sum1 + 1);
  ll qq = count_ge(sum2 + 1);
  ll slot = p - pp;
  std::vector<std::pair<int, int>> extra;
  ll ans1 = 0;
  treap::init();
  for (int i = n - 1; i >= 0; --i) {
    treap::node *a = 0, *b = 0, *c = 0;
    std::tie(b, c) = treap::split(treap::rt, sum[i] - sum1);
    std::tie(a, b) = treap::split(b, sum[i] - sum1 - 1);
    if (a) {
      cov[i] = std::max(cov[i], a->mx);
      ans1 += sum[i] * a->sz - a->sum;
    }
    if (b) {
      int need = std::min<ll>(slot, b->sz);
      treap::node *x, *y;
      std::tie(x, y) = split_by_size(b, need);
      if (x) {
        cov[i] = std::max(cov[i], x->mx);
        ans1 += sum[i] * x->sz - x->sum;
      }
      trans(y, extra, q, i);
      b = treap::merge(x, y);
      slot -= need;
    }
    treap::rt = treap::merge(treap::merge(a, b), c);
    treap::add(i, sum[i]);
  }
  if (extra.size() < q) {
    treap::init();
    slot = m - qq;
    for (int i = n - 1; i >= 0; --i) {
      treap::node *a = 0, *b = 0, *c = 0, *d = 0;
      std::tie(d, c) = treap::split(treap::rt, sum[i] - sum1);
      std::tie(b, c) = treap::split(c, sum[i] - sum2);
      std::tie(a, b) = treap::split(b, sum[i] - sum2 - 1);
      if (a) trans(a, extra, q, i);
      if (b) {
        int need = std::min<ll>(slot, b->sz);
        treap::node *x, *y;
        std::tie(x, y) = split_by_size(b, need);
        if (x) trans(x, extra, q, i);
        b = treap::merge(x, y);
        slot -= need;
      }
      treap::rt = treap::merge(treap::merge(d, a), treap::merge(b, c));
      treap::add(i, sum[i]);
    }
  }
  assert(extra.size() == q);
  std::sort(extra.begin(), extra.end(),
            [&](const std::pair<int, int> &a, const std::pair<int, int> &b) {
              return sum[a.first] - sum[a.second + 1] >
                     sum[b.first] - sum[b.second + 1];
            });
  std::vector<int> mark(n + 1, 0);
  std::set<int> uncovered;
  kth::init(q - 1);
  int last = -1;
  for (int i = 0; i < n; ++i) {
    if (cov[i] != -1) mark[i]++, mark[cov[i]]--;
    if (i) mark[i] += mark[i - 1];
    if (!mark[i]) {
      if (last != -1) kth::add(get(last, i));
      uncovered.insert(i);
      last = i;
    }
  }
  ll ret = -inf;
  for (int i = 0; i <= q; ++i) {
    int rest = q - i;
    if (rest <= uncovered.size()) {
      ll ans2 = 0;
      if (uncovered.size() && rest) {
        int x = *uncovered.begin();
        int y = *uncovered.rbegin();
        ans2 = max_sum[x] - min_sum[y + 1];
      }
      if (rest || uncovered.empty()) {
        ret = std::max(ret, ans1 + ans2 - kth::sum);
      }
    }
    if (i == q) break;
    int l = extra[i].first, r = extra[i].second;
    int x = -1, y = -1;
    ans1 += sum[l] - sum[r + 1];
    std::vector<int> rm;
    auto it = uncovered.lower_bound(l);
    if (it != uncovered.begin()) --it, x = *it, ++it;
    for (; it != uncovered.end() && *it <= r;) {
      rm.push_back(*it);
      it = uncovered.erase(it);
    }
    if (it != uncovered.end()) y = *it;
    if (rm.size()) {
      if (x != -1) kth::del(get(x, rm[0]));
      if (y != -1) kth::del(get(rm.back(), y));
      for (size_t j = 1; j < rm.size(); ++j) {
        kth::del(get(rm[j - 1], rm[j]));
      }
    }
    if (x != -1 && y != -1 && !rm.empty()) kth::add(get(x, y));
    kth::reduce();
  }
  printf("%lld\n", ret);
  return 0;
}