Problem p03032 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;

template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
template <class T> using VVV = V<VV<T>>;
template <class S, class T> using P = pair<S, T>;
template <class S, class T, class U> using TP = tuple<S, T, U>;

using ll = long long;
using ull = unsigned long long;
using dbl = double;
using str = string;
using vll = V<ll>;
using vvll = V<vll>;
using vvvll = V<vvll>;
using pl = P<ll, ll>;
using tl = TP<ll, ll, ll>;
using vpl = V<pl>;
using vvpl = V<vpl>;
using vtl = V<tl>;
using vvtl = V<vtl>;
using vs = V<str>;
using vvs = V<vs>;
using vd = V<dbl>;
using vvd = V<vd>;
using qll = queue<ll>;
using qpl = queue<pl>;
using stll = stack<ll>;
using stpl = stack<pl>;
using mapll = map<ll, ll>;
using setll = set<ll>;
using pqll = priority_queue<ll>;

#define int ll
#define fi first
#define se second
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pob pop_back()
#define pf push_front
#define pof pop_front()
#define sz size()
#define bgn begin()
#define en end()
#define asn assign
#define emp empty()
#define fr front()
#define bk back()
#define clr clear()
#define ins insert
#define ers erase
#define res resize
#define tp top()
#define p_q priority_queue
#define inv inverse()

#define FOR(i, a, b) for (ll i = (a); i <= (ll)(b); i++)
#define rFOR(i, a, b) for (ll i = (b); i >= (ll)(a); i--)
#define REP(i, a) FOR((i), 0, (ll)(a)-1)
#define REP0(i, a) FOR((i), 0, (ll)(a))
#define REP1(i, a) FOR((i), 1, (ll)(a))
#define rREP(i, a) rFOR((i), 0, (ll)(a)-1)
#define rREP0(i, a) rFOR((i), 0, (ll)(a))
#define rREP1(i, a) rFOR((i), 1, (ll)(a))
#define ROR(v, i) for (auto &(i) : (v))
#define IOTA(a, n) iota((a).bgn, (a).en, (n))
#define SORT(a) sort((a).bgn, (a).en)
#define rSORT(a) sort((a).rbegin(), (a).rend())
#define UNIQUE(a) (a).erase(unique((a).bgn, (a).en), (a).en)
#define PREVP(a) prev_permutation((a).bgn, (a).en)
#define NEXTP(a) next_permutation((a).bgn, (a).en)
#define BINS(a, b) binary_search((a).bgn, (a).en, (b))
#define LOWB(a, b) (lower_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define UPB(a, b) (upper_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define CNT(a, b) count((a).bgn, (a).en, b)
#define SUM(a) accumulate((a).bgn, (a).en, 0)
#define REV(a) reverse((a).bgn, (a).en)
#define REGS(a, b) regex_search((a), regex(b))
#define REGM(a, b) regex_match((a), regex(b))
#define yn(a) cout << ((a) ? "yes" : "no") << "\n";
#define Yn(a) cout << ((a) ? "Yes" : "No") << "\n";
#define YN(a) cout << ((a) ? "YES" : "NO") << "\n";
#define imp(a) cout << ((a) ? "possible" : "impossible") << "\n";
#define Imp(a) cout << ((a) ? "Possible" : "Impossible") << "\n";
#define IMP(a) cout << ((a) ? "POSSIBLE" : "IMPOSSIBLE") << "\n";
#define fs(a) cout << ((a) ? "second" : "first") << "\n";
#define Fs(a) cout << ((a) ? "Second" : "First") << "\n";
#define FS(a) cout << ((a) ? "SECOND" : "FIRST") << "\n";
#define sak cout << "\n";
#define sas cout << " ";
#define sat cout << "\t";
#define dbg(a) cerr << (#a) << ": " << (a) << "\n";
#define dbgs(...)                                                              \
  dal(#__VA_ARGS__);                                                           \
  dal(__VA_ARGS__);
#define c2l(a) ((ll)(a - 48))
#define a2l(a) ((ll)(a - 97))
#define A2l(a) ((ll)(a - 65))
#define l2c(a) ((char)(a + 48))
#define l2a(a) ((char)(a + 97))
#define l2A(a) ((char)(a + 65))
#define DigN2(a) ((llabs(a) == 0) ? (1) : ((ll)(log2(double(llabs(a)))) + 1))
#define DigN10(a) ((llabs(a) == 0) ? (1) : ((ll)(log10(double(llabs(a)))) + 1))
#define Dig2(a, b) (((a) >> (b)) & 1)
#define Dig10(a, b) (ll)(((a) / ((ll)(pow(10.0, (double)(b))))) % 10)
#define Pow2(a) ((ll)(1) << (a))
#define Pow10(a) ((ll)(pow(10.0, double(a))))
#define LSB(a) ((a) & (-(a)))
#define vin(v)                                                                 \
  ROR((v), (i)) { cin >> (i); };
#define vllin(v, N)                                                            \
  vll(v)((N));                                                                 \
  vin(v);
#define vllin2(a, b, N)                                                        \
  vll(a)(N), (b)(N);                                                           \
  REP(i, N) { cin >> (a)[i] >> (b)[i]; };
#define vsin(v, N)                                                             \
  vs(v)((N));                                                                  \
  vin(v);
#define rdn(a, b) ((a) / (b))
#define rou(a, b)                                                              \
  ((((double(a) / double(b)) - ((a) / (b))) < 0.5) ? ((a) / (b))               \
                                                   : (((a) / (b)) + 1))
#define rup(a, b) ((((a) % (b)) == 0) ? ((a) / (b)) : (((a) / (b)) + 1))
#define min(...) Min(__VA_ARGS__)
#define max(...) Max(__VA_ARGS__)
#define emin(a, ...) ((a) = Min((a), __VA_ARGS__))
#define emax(a, ...) ((a) = Max((a), __VA_ARGS__))
#define egcd(a, ...) ((a) = gcd((a), __VA_ARGS__))
#define elcm(a, ...) ((a) = lcm((a), __VA_ARGS__))
#define powll(a, b) (ll)(pow((double)(a), (double)(b)))
#define Triangle(x1, y1, x2, y2, x3, y3)                                       \
  (((x1) - (x2)) * ((y1) - (y3)) - ((x1) - (x3)) * ((y1) - (y2)))

#define svll SumV<ll>
#define svvll SumV2<ll>

#define li(...)                                                                \
  ll __VA_ARGS__;                                                              \
  Input(__VA_ARGS__);
#define si(...)                                                                \
  str __VA_ARGS__;                                                             \
  Input(__VA_ARGS__);
#define vli(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInput(size, __VA_ARGS__);
#define vsi(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInput(size, __VA_ARGS__);

// const ll MOD = 1e9 + 7;
const ll MOD = 998244353;
// const ll MOD = 924844033;
// const ll MOD = 9007199254740881;
const ll INF = 1LL << 60; // 1.15e18
const double PI = acos(-1.0);
const vll DX = {0, -1, 0, 1, 0, -1, 1, 1, -1};
const vll DY = {0, 0, -1, 0, 1, -1, -1, 1, 1};
const str alp = "abcdefghijklmnopqrstuvwxyz";
const str ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

void Input() {}
template <class Var, class... Args> void Input(Var &var, Args &...args) {
  cin >> var;
  Input(args...);
}

void vInit(ll size) {}
template <class T, class... Args> void vInit(ll size, V<T> &v, Args &...args) {
  v.res(size);
  vInit(size, args...);
}
void vInputNum(ll num) {}
template <class T, class... Args>
void vInputNum(ll num, V<T> &v, Args &...args) {
  cin >> v[num];
  vInputNum(num, args...);
}
void vInput(ll size) {}
template <class... Args> void vInput(ll size, Args &...args) {
  vInit(size, args...);
  REP(i, size) vInputNum(i, args...);
}

template <class S, class T>
ostream &operator<<(ostream &out, const P<S, T> &p) {
  return out << "[" << p.fi << ", " << p.se << "]";
}

template <class T> ostream &operator<<(ostream &out, V<T> &v) {
  if (v.emp)
    return out << "{}";
  else {
    auto itr = v.bgn;
    out << "{" << *itr;
    itr++;
    while (itr != v.en) {
      out << ", " << *itr;
      itr++;
    }
    out << "}";
    return out;
  }
}

template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> &m) {
  if (m.emp)
    return out << "<[]>";
  else {
    auto itr = m.bgn;
    out << "< [" << (itr->fi) << ": " << (itr->se);
    itr++;
    while (itr != m.en) {
      out << "], [" << (itr->fi) << ": " << (itr->se);
      itr++;
    }
    out << "] >";
    return out;
  }
}

template <class T> ostream &operator<<(ostream &out, const set<T> &s) {
  if (s.emp)
    return out << "<>";
  else {
    auto itr = s.bgn;
    out << "<" << *itr;
    itr++;
    while (itr != s.en) {
      out << ", " << *itr;
      itr++;
    }
    out << ">";
    return out;
  }
}

void say() {}
template <class T> void say(T t) { cout << t; }
template <class Head, class... Body> void say(Head head, Body... body) {
  cout << head << " ";
  say(body...);
}
void sal() { cout << "\n"; }
template <class... Args> void sal(Args... args) {
  say(args...);
  cout << "\n";
}

void day() {}
template <class T> void day(T t) { cerr << t; }
template <class Head, class... Body> void day(Head head, Body... body) {
  cerr << head << " ";
  day(body...);
}
void dal() { cerr << "\n"; }
template <class... Args> void dal(Args... args) {
  day(args...);
  cerr << "\n";
}

void salv() {}
template <class T> void salv(V<T> v) {
  if (v.emp)
    sal();
  else {
    auto itr = v.bgn;
    say(*itr);
    itr++;
    while (itr != v.en) {
      sas;
      say(*itr);
      itr++;
    }
    sak;
  }
}
template <class T, class... Args> void salv(V<T> v, Args... args) {
  salv(v);
  salv(args...);
}

void salv2() {}
template <class T> void salv2(V<V<T>> v) {
  if (v.emp)
    sal();
  else {
    ROR(v, i) salv(i);
  }
}
template <class T, class... Args> void salv2(V<V<T>> v, Args... args) {
  salv2(v);
  salv2(args...);
}

template <class Monoid> struct Action {
public:
  Monoid I;
  function<Monoid(Monoid, Monoid)> A;
  Action(Monoid I, function<Monoid(Monoid, Monoid)> A) : I(I), A(A) {}
  Monoid operator()() { return I; }
  Monoid operator()(Monoid x) { return x; }
  Monoid operator()(Monoid l, Monoid r) { return A(l, r); }
  template <class... Args> Monoid operator()(Monoid x, Args... args) {
    Monoid tmp = operator()(args...);
    return A(x, tmp);
  }
};

template <class T> Action<T> ADD = Action<T>(0, [](T l, T r) { return l + r; });
template <>
Action<str> ADD<str> = Action<str>("", [](str l, str r) { return l + r; });
template <class T1, class T2>
Action<P<T1, T2>> ADD<P<T1, T2>> =
    Action<P<T1, T2>>(mp(ADD<T1>.I, ADD<T2>.I), [](P<T1, T2> l, P<T1, T2> r) {
      return mp(l.fi + r.fi, l.se + r.se);
    });

template <class T> Action<T> MUL = Action<T>(1, [](T l, T r) { return l * r; });
template <class T> Action<T> OR = Action<T>(0, [](T l, T r) { return l | r; });
template <class T> Action<T> XOR = Action<T>(0, [](T l, T r) { return l ^ r; });

template <class T>
Action<T> AND = Action<T>(((ll)(1) << 63) - 1, [](T l, T r) { return l & r; });
template <>
Action<bool> AND<bool> =
    Action<bool>(true, [](bool l, bool r) { return l & r; });
template <>
Action<ull> AND<ull> =
    Action<ull>(((ull)(1) << 63) - 1, [](ull l, ull r) { return l & r; });

template <class T>
Action<T> MIN = Action<T>(INF, [](T l, T r) { return (l < r) ? l : r; });
template <class T>
Action<T> MAX = Action<T>(-INF, [](T l, T r) { return (l > r) ? l : r; });

template <class T>
Action<T> GCD = Action<T>(0, [](T l, T r) {
  if (l < r) {
    l ^= r;
    r ^= l;
    l ^= r;
  }
  return (r ? GCD<T>(r, l % r) : l);
});
template <class T>
Action<T> LCM = Action<T>(1, [](T l, T r) { return (l * r) / GCD<T>(l, r); });

template <class Head> Head Min(Head head) { return head; }
template <class Head, class... Body> Head Min(Head head, Body... body) {
  auto tmp = Min(body...);
  return (head < tmp) ? head : tmp;
}

template <class Head> Head Max(Head head) { return head; }
template <class Head, class... Body> auto Max(Head head, Body... body) {
  auto tmp = Max(body...);
  return (head > tmp) ? head : tmp;
}

ll gcd(ll a, ll b) {
  if (a < b) {
    a ^= b;
    b ^= a;
    a ^= b;
  }
  return b ? gcd(b, a % b) : a;
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

ll gcd(ll head) { return head; }
template <class... Body> ll gcd(ll head, Body... body) {
  return gcd(head, gcd(body...));
}

ll lcm(ll head) { return head; }
template <class... Body> ll lcm(ll head, Body... body) {
  return lcm(head, lcm(body...));
}

ll Bset(ll a, ll b, ll c) {
  if (c)
    a |= b;
  else
    a &= ~b;
  return a;
}

struct UFT {

public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  UFT() {}
  UFT(const UFT &uft) {}
  UFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
  }
  ll root(ll x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

struct pUFT {

public:
  ll tsize;
  ll now;
  vll par;
  vll rank;
  vll mtime;
  vvll sizepi;
  vvll sizepv;

  pUFT() {}
  pUFT(const pUFT &puft) {}

  pUFT(ll tsizeget) {
    tsize = tsizeget;
    now = 0;
    par.asn(tsize, -1);
    rank.asn(tsize, 0);
    mtime.asn(tsize, INF);
    sizepi.asn(tsize, {0});
    sizepv.asn(tsize, {1});
  }
  ll root(ll x, ll t) { return (mtime[x] > t) ? x : root(par[x], t); }
  bool same(ll x, ll y, ll t) { return root(x, t) == root(y, t); }
  ll merge(ll x, ll y) {
    now++;
    x = root(x, now);
    y = root(y, now);
    if (x != y) {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        sizepi[y].pb(now);
        sizepv[y].pb(-par[y]);
        par[x] = y;
        mtime[x] = now;
      } else {
        par[x] += par[y];
        sizepi[x].pb(now);
        sizepv[x].pb(-par[x]);
        par[y] = x;
        mtime[y] = now;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
    return now;
  }
  ll size(ll x, ll t) {
    x = root(x, t);
    return sizepv[x][UPB(sizepi[x], t) - 1];
  }
};

struct wUFT {
public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  vll dweight;
  wUFT() {}
  wUFT(const wUFT &wuft) {}
  wUFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
    dweight.asn(tsize, 0);
  }
  ll root(ll x) {
    if (par[x] < 0)
      return x;
    else {
      ll r = root(par[x]);
      dweight[x] += dweight[par[x]];
      return par[x] = r;
    }
  }
  ll weight(ll x) {
    root(x);
    return dweight[x];
  }
  ll diff(ll x, ll y) { return weight(y) - weight(x); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y, ll w) {
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
        dweight[x] = -w;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
        dweight[y] = w;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

template <typename valtype> class SegT {

public:
  ll size;
  vector<valtype> v;

  valtype initv;
  function<valtype(valtype x, valtype y)> calc;

  SegT() {}
  SegT(const SegT &segt) {}

  SegT(ll sizeget, ll modeget = 0) {
    sizeset(sizeget);
    modeset(modeget);
    init();
  }
  SegT(vector<valtype> cpyvec, ll modeget = 0) {
    sizeset(cpyvec.sz);
    modeset(modeget);
    init();
    copy(cpyvec);
  }
  SegT(ll sizeget, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(sizeget);
    initv = initvget;
    calc = calcget;
    init();
  }
  SegT(vector<valtype> cpyvec, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(cpyvec.sz);
    initv = initvget;
    calc = calcget;
    init();
    copy(cpyvec);
  }
  void sizeset(ll rsize) {
    size = DigN2(rsize);
    if (rsize == Pow2(size - 1))
      size--;
    return;
  }
  void modeset(ll mode) {
    switch (mode) {
    case 0:
      initv = 0;
      calc = [](valtype x, valtype y) { return x + y; };
      break;
    case 1:
      initv = INF;
      calc = [](valtype x, valtype y) { return min(x, y); };
      break;
    case 2:
      initv = -INF;
      calc = [](valtype x, valtype y) { return max(x, y); };
      break;
    }
    return;
  }
  void init() { v.asn(Pow2(size + 1) - 1, initv); }
  void copy(vector<valtype> cpyvec) {
    REP(i, min(cpyvec.sz, Pow2(size))) set(i, cpyvec[i]);
  }
  ll i2v(ll i) const {
    if (i < 0 || i >= Pow2(size))
      return -1;
    return Pow2(size) + i - 1;
  }
  ll top(ll i) const {
    if (i == 0)
      return -1;
    return (i - 1) / 2;
  }
  pl bot(ll i) const {
    if (i + 1 >= Pow2(size))
      return mp(-1, -1);
    return mp(2 * i + 1, 2 * i + 2);
  }
  void set(ll i, valtype x) {
    i = i2v(i);
    v[i] = x;
    while (i > 0) {
      i = top(i);
      v[i] = calc(v[bot(i).fi], v[bot(i).se]);
    }
    return;
  }
  void add(ll i, valtype x) {
    set(i, v[i2v(i)] + x);
    return;
  }
  valtype operator[](const ll &i) const { return v[i2v(i)]; }
  //  valtype que(ll a = 0, ll b = Pow2(size) - 1) {
  valtype que(ll a, ll b) {
    if (a == b)
      return v[i2v(a)];
    if (a > b)
      return initv; // swap(a, b);
    valtype ans = initv;
    ll ai = i2v(a);
    ll bi = i2v(b);
    FOR(i, 1, size + 1) {
      if (a > b)
        break;
      if (a % Pow2(i)) {
        ans = calc(ans, v[ai]);
        a += Pow2(i - 1);
        ai = top(ai) + 1;
      } else {
        ai = top(ai);
      }
      if (a > b)
        break;
      if ((b + 1) % Pow2(i)) {
        ans = calc(ans, v[bi]);
        b -= Pow2(i - 1);
        bi = top(bi) - 1;
      } else {
        bi = top(bi);
      }
      if (a > b)
        break;
    }
    return ans;
  }
  valtype que(ll b) { return que(0, b); }
  valtype que() { return que(0, Pow2(size) - 1); }
};

template <typename lentype> class Graph {

public:
  ll size;
  ll mode;
  ll mapmode;
  lentype zlen;
  lentype ilen;
  vector<map<ll, ll>> v2n;
  vvll n2v;
  vector<vector<lentype>> Edge;
  vector<pair<lentype, ll>> Primresult;

  Graph() {}
  Graph(const Graph &graph) {}

  Graph(ll sizeget = 0, ll mapmodeget = 0, ll modeget = 0, lentype zlenget = 0,
        lentype ilenget = INF) {
    size = sizeget;
    mapmode = mapmodeget;
    mode = modeget;
    zlen = zlenget;
    ilen = ilenget;
    init();
  }
  void init() {
    Edge.res(size);
    v2n.res(size);
    n2v.res(size);
    Primresult.asn(size, mp(ilen, -1));
  }
  lentype lenplus(lentype l, lentype r) { return l + r; }
  lentype lenequal(lentype l, lentype r) { return l == r; }
  lentype lenlcr(lentype l, lentype r) { return l < r; }
  ll addV(ll vs) {
    size += vs;
    init();
    return size;
  }
  void caddE(ll x, ll y, lentype c) {
    if (mapmode)
      v2n[x][y] = Edge[x].sz;
    Edge[x].pb(c);
    n2v[x].pb(y);
  }
  void csetE(ll x, ll y, lentype c) {
    if (mapmode)
      Edge[x][v2n[x][y]] = c;
  }
  void cersE(ll x, ll y) {
    if (mapmode) {
      ll n = v2n[x][y];
      Edge[x][n] = ilen;
      n2v[x][n] = -1;
      v2n[x].ers(y);
    }
  }
  void addE(ll x, ll y, lentype c) {
    caddE(x, y, c);
    if (!mode)
      caddE(y, x, c);
  }
  void setE(ll x, ll y, lentype c) {
    csetE(x, y, c);
    if (!mode)
      csetE(y, x, c);
  }
  void ersE(ll x, ll y, lentype c) {
    cersE(x, y, c);
    if (!mode)
      cersE(y, x, c);
  }
  lentype getE(ll x, ll y) {
    if (mapmode) {
      if (v2n[x].count(y)) {
        return Edge[x][v2n[x][y]];
      }
    }
    return ilen;
  }
  ll getVsz(ll x) { return Edge[x].sz; }
  pair<lentype, ll> getV(ll x, ll n) {
    if (n >= getVsz(x))
      return mp(ilen, -1);
    return mp(Edge[x][n], n2v[x][n]);
  }

  vector<pair<lentype, vll>> Dijk(ll x) {
    vector<pair<lentype, vll>> result(size);
    REP(i, size) {
      result[i].fi = ilen;
      result[i].se = {-1};
    }
    vll stat(size, 0);
    pair<lentype, ll> now;
    pair<lentype, ll> nowlv;
    SegT<pair<lentype, ll>> Q(size, mp(ilen, -1),
                              [](pair<lentype, ll> l, pair<lentype, ll> r) {
                                if (l.se == -1)
                                  return r;
                                if (r.se == -1)
                                  return l;
                                return l.fi < r.fi ? l : r;
                              });
    Q.set(x, mp(zlen, x));
    result[x].fi = zlen;
    result[x].se = {-1};
    while (Q.que(0, size - 1).se != -1) {
      now = Q.que(0, size - 1);
      Q.set(now.se, mp(ilen, -1));
      stat[now.se] = 1;
      REP(i, getVsz(now.se)) {
        nowlv = getV(now.se, i);
        if (stat[nowlv.se])
          continue;
        if (Q[nowlv.se].se == -1) {
          result[nowlv.se].fi = lenplus(result[now.se].fi, nowlv.fi);
          result[nowlv.se].se = {now.se};
          Q.set(nowlv.se, mp(result[nowlv.se].fi, nowlv.se));
        } else {
          if (lenlcr(lenplus(result[now.se].fi, nowlv.fi),
                     result[nowlv.se].fi)) {
            result[nowlv.se].fi = lenplus(result[now.se].fi, nowlv.fi);
            result[nowlv.se].se = {now.se};
            Q.set(nowlv.se, mp(result[nowlv.se].fi, nowlv.se));
          } else if (lenequal(lenplus(result[now.se].fi, nowlv.fi),
                              result[nowlv.se].fi)) {
            result[nowlv.se].se.pb(now.se);
          }
        }
      }
    }
    return result;
  }

  lentype Prim(ll x = 0) {
    lentype ans = zlen;
    vll stat(size, 0);
    pair<lentype, ll> now;
    pair<lentype, ll> nowlv;
    SegT<pair<lentype, ll>> Q(size, mp(ilen, -1),
                              [](pair<lentype, ll> l, pair<lentype, ll> r) {
                                if (l.se == -1)
                                  return r;
                                if (r.se == -1)
                                  return l;
                                return l.fi < r.fi ? l : r;
                              });
    Q.set(x, mp(zlen, x));
    Primresult[x] = mp(zlen, -1);
    while (Q.que(0, size - 1).se != -1) {
      now = Q.que(0, size - 1);
      Q.set(now.se, mp(ilen, -1));
      stat[now.se] = 1;
      ans = lenplus(ans, Primresult[now.se].fi);
      REP(i, getVsz(now.se)) {
        nowlv = getV(now.se, i);
        if (stat[nowlv.se])
          continue;
        if (Q[nowlv.se].se == -1) {
          Primresult[nowlv.se] = mp(nowlv.fi, now.se);
          Q.set(nowlv.se, mp(Primresult[nowlv.se].fi, nowlv.se));
        } else {
          if (lenlcr(nowlv.fi, Primresult[nowlv.se].fi)) {
            Primresult[nowlv.se] = mp(nowlv.fi, now.se);
            Q.set(nowlv.se, mp(Primresult[nowlv.se].fi, nowlv.se));
          }
        }
      }
    }
    return ans;
  }
};

/*template <class Type> class DP {

public:

    vector<Type> v;
    Type initv;
    vll size, block;

    DP() {}
    DP(const DP &dp) {}

    template<class... Args> DP(Args... args) {
        block.asn(1, 1);
        Initialize(args...);
    }

    void Initialize(Type initv_) {
        initv = initv_;
        v.asn(block.bk, initv);
    }
    template<class... Args> void Initialize(ll val, Args... args) {
        size.pb(val);
        block.pb(block.bk*val);
        Initialize(args...);
    }



};*/

pl Bezout(ll a, ll b) {
  if (b != 0) {
    pl xy;
    xy = Bezout(b, a % b);
    return mp(xy.se, xy.fi - ((a / b) * xy.se));
  } else {
    return mp(1, 0);
  }
}
pl Bez(ll a, ll b, ll c) {
  pl xy;
  ll x, y, z, gc;
  xy = Bezout(a, b);
  gc = gcd(a, b);
  if (c % gc != 0)
    return mp(-1, -1);
  x = xy.fi * (c / gc);
  y = xy.se * (c / gc);
  if (x < 0)
    z = rup(-x, (b / gc));
  if (x >= 0)
    z = -x / (b / gc);
  x += z * (b / gc);
  y -= z * (a / gc);
  return mp(x, y);
}

ll DigS10(ll n) {
  ll ans = 0;
  while (1) {
    ans += n % 10;
    n /= 10;
    if (!n)
      break;
  }
  return ans;
}

ll isP(ll n) {
  if (n <= 1)
    return 0;
  FOR(i, 2, (ll)sqrt(n) + 1) {
    if (n % i == 0)
      return 0;
  }
  return 1;
}

ll Tot(ll n) {
  if (n <= 0)
    return 0;
  ll ans = n, x = 2;
  while (x * x <= n) {
    if (n % x == 0) {
      ans -= ans / x;
      while (n % x == 0)
        n /= x;
    }
    x++;
  }
  if (n > 1)
    ans -= ans / n;
  return ans;
}

template <class T> struct Sum {
public:
  V<T> v, s;
  ll size;
  Action<T> Add;
  Sum(V<T> v, Action<T> Add = ADD<T>) : v(v), size(v.sz), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(size + 1, Add.I); }
  void Calc() { REP(i, size) s[i + 1] = Add(s[i], v[i]); }
  T operator()(ll x) { return operator()(0, x); }
  T operator()(ll l, ll r) {
    if (l < 0)
      l = 0;
    if (r >= size)
      r = size - 1;
    if (l > r)
      return Add.I;
    return s[r + 1] - s[l]; // for ADD
  }
};
using sumll = Sum<ll>;

template <class T> struct Sum2 {
public:
  V<V<T>> v, s;
  ll RowSize, ColumnSize;
  Action<T> Add;
  Sum2(V<V<T>> v, Action<T> Add = ADD<T>)
      : v(v), RowSize(v.sz), ColumnSize(v.sz ? v[0].sz : 0), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(RowSize + 1, V<T>(ColumnSize, Add.I)); }
  void Calc() {
    REP1(r, RowSize) {
      REP1(c, ColumnSize) {
        s[r][c] =
            v[r - 1][c - 1] + operator()(r, c - 1) + operator()(r - 1, c) -
                                                     operator()(r - 1, c - 1);
      }
    }
  }
  T operator()(ll r, ll c) { return operator()(0, 0, r, c); }
  T operator()(ll r1, ll c1, ll r2, ll c2) {
    if (r1 < 0)
      r1 = 0;
    if (c1 < 0)
      c1 = 0;
    if (r2 >= RowSize)
      r2 = RowSize - 1;
    if (c2 >= ColumnSize)
      c2 = ColumnSize - 1;
    if (r1 > r2)
      return Add.I;
    if (c1 > c2)
      return Add.I;
    return s[r2 + 1][c2 + 1] - s[r2 + 1][c1] - s[r1][c2 + 1] + s[r1][c1];
  }
};
using sum2ll = Sum2<ll>;

template <class T> struct Point2 {
public:
  V<V<T>> v;
  ll h, w;
  Point2() : h(0), w(0) {}
  Point2(ll h, ll w) : h(h), w(w) { asn(h, w); }
  Point2(ll h, ll w, T val) : h(h), w(w) { asn(h, w, val); }
  void assign(ll h, ll w) { v.asn(h, V<T>(w)); }
  void assign(ll h, ll w, ll val) { v.asn(h, V<T>(w, val)); }
  T &operator()(ll h, ll w) { return v[h][w]; }
  T &operator()(pl p) { return v[p.fi][p.se]; }
};
template <class T> using P2 = Point2<T>;

template <ll Mod> struct Modll {
public:
  ll v;
  Modll() : v(0) {}
  Modll(ll _v) { set(_v % Mod + Mod); }
  Modll &set(ll _v) {
    v = (_v < Mod) ? _v : (_v - Mod);
    return *this;
  }
  Modll pow(ll n) const {
    Modll x = *this, ans = 1;
    while (n) {
      if (n & 1)
        ans *= x;
      x *= x;
      n >>= 1;
    }
    return ans;
  }
  Modll inverse() const { return (*this).pow(Mod - 2); }
  Modll operator+(const Modll &m) const { return Modll().set(v + m.v); }
  Modll operator-(const Modll &m) const { return Modll().set(Mod + v - m.v); }
  Modll operator*(const Modll &m) const {
    return Modll().set((ull(v) * m.v) % Mod);
  }
  Modll operator/(const Modll &m) const { return *this * m.inv; }
  Modll &operator+=(const Modll &m) { return *this = *this + m; }
  Modll &operator-=(const Modll &m) { return *this = *this - m; }
  Modll &operator*=(const Modll &m) { return *this = *this * m; }
  Modll &operator/=(const Modll &m) { return *this = *this / m; }
  Modll operator-() const { return Modll(0) - *this; }
  explicit operator bool() const { return v != 0; }
  friend ostream &operator<<(ostream &out, const Modll &m) {
    return out << m.v;
  }
};
using mll = Modll<MOD>;
using vmll = V<mll>;
using vvmll = V<vmll>;
using vvvmll = V<vvmll>;

template <class T> T vmin(V<T> v) {
  T tmp = MIN<T>.I;
  ROR(v, i) emin(tmp, i);
  return tmp;
}
template <class T, class... Args> T vmin(V<T> v, Args... args) {
  T tmp = vmin(args...);
  return min(vmin(v), tmp);
}

template <class T> T vmax(V<T> v) {
  T tmp = MAX<T>.I;
  ROR(v, i) emax(tmp, i);
  return tmp;
}
template <class T, class... Args> T vmax(V<T> v, Args... args) {
  T tmp = vmax(args...);
  return max(vmax(v), tmp);
}

template <class T> T vgcd(V<T> v) {
  T tmp = GCD<T>.I;
  ROR(v, i) egcd(tmp, i);
  return tmp;
}
template <class T, class... Args> T vgcd(V<T> v, Args... args) {
  T tmp = vgcd(args...);
  return gcd(vgcd(v), tmp);
}

template <class T> T vlcm(V<T> v) {
  T tmp = LCM<T>.I;
  ROR(v, i) elcm(tmp, i);
  return tmp;
}
template <class T, class... Args> T vlcm(V<T> v, Args... args) {
  T tmp = vlcm(args...);
  return lcm(vlcm(v), tmp);
}

vmll MFactMemo(2, 1);
vmll MIFactMemo(2, 1);

mll mFact(ll n) {
  if (MFactMemo.sz <= n) {
    ll oldsize = MFactMemo.sz;
    MFactMemo.res(n + 1, 1);
    FOR(i, oldsize, n) MFactMemo[i] = MFactMemo[i - 1] * i;
  }
  return MFactMemo[n];
}
mll miFact(ll n) {
  if (MIFactMemo.sz <= n) {
    ll oldsize = MIFactMemo.sz;
    MIFactMemo.res(n + 1, 1);
    MIFactMemo.bk = mFact(n).inv;
    rFOR(i, oldsize + 1, n) MIFactMemo[i - 1] = MIFactMemo[i] * i;
  }
  return MIFactMemo[n];
}
mll mComb(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return mFact(n) * miFact(k) * miFact(n - k);
}

ll LIS(vll v, ll m = 0) {

  if (v.sz > 0) {
    ll ans = 0;
    vll dp(v.sz, INF);
    FOR(i, 0, v.sz - 1) { dp[m ? UPB(dp, v[i]) : LOWB(dp, v[i])] = v[i]; }
    FOR(i, 0, v.sz - 1) {
      if (dp[i] == INF)
        break;
      ans++;
    }
    return ans;
  } else {
    return 0;
  }
}

void PCmprs(vll &v) {
  if (v.sz == 0)
    return;
  vll vv(v);
  IOTA(vv, 0);
  sort(vv.bgn, vv.en, [&](ll v1, ll v2) { return v[v1] < v[v2]; });
  IOTA(v, 0);
  sort(v.bgn, v.en, [&](ll v1, ll v2) { return vv[v1] < vv[v2]; });
  return;
}

ll BblCnt(vll v) {
  PCmprs(v);
  SegT<ll> b(v.sz, 0);
  ll ans = 0;
  REP(i, v.sz) {
    ans += (i - b.que(0, v[i]));
    b.add(v[i], 1);
  }
  return ans;
}

ll Bsrch(function<bool(ll x)> f, ll mi, ll ma) {
  ll ng = mi - 1, ok = ma, mid;
  while (ok - ng > 1) {
    mid = (ng + ok) / 2;
    (f(mid) ? ok : ng) = mid;
  }
  return ok;
}

template <class T>
V<V<T>> MultiMatrix(V<V<T>> A, V<V<T>> B, Action<T> Mul = MUL<T>,
                    Action<T> Add = ADD<T>) {
  V<V<T>> ans;
  ll ii = A.sz;
  if (!ii)
    return ans;
  ll jj = A[0].sz;
  if (!jj)
    return ans;
  ll jj2 = B.sz;
  if (!jj2)
    return ans;
  if (jj != jj2)
    return ans;
  ll kk = B[0].sz;
  if (!kk)
    return ans;
  ans.asn(ii, V<T>(kk, 0));
  REP(i, ii) {
    REP(k, kk) {
      REP(j, jj) { ans[i][k] = Add(ans[i][k], Mul(A[i][j], B[j][k])); }
    }
  }
  return ans;
}

vvll CombMemo(1000, vll(1000, -1));

ll Comb(ll n, ll k) {
  if ((n < 0) || (k < 0))
    return 0;
  if (CombMemo[n][k] == -1) {
    if (n < k)
      CombMemo[n][k] = 0;
    else {
      if (n == 0)
        CombMemo[n][k] = 1;
      else if (k == 0)
        CombMemo[n][k] = 1;
      else if (n == k)
        CombMemo[n][k] = 1;
      else
        CombMemo[n][k] = Comb(n - 1, k - 1) + Comb(n - 1, k);
    }
  }
  return CombMemo[n][k];
}

template <class T> map<T, ll> Dict(V<T> v) {
  map<T, ll> m;
  if (!v.sz)
    return m;
  SORT(v);
  UNIQUE(v);
  REP(i, v.sz) { m[v[i]] = i; }
  return m;
}

template <class T> vll Cmprs(V<T> v) {
  auto m = Dict(v);
  vll ans(v.sz);
  REP(i, v.sz) { ans[i] = m[v[i]]; }
  return ans;
}

template <class T> auto vecn(T val) { return val; }
template <class... Args> auto vecn(ll val, Args... args) {
  auto tmp = vecn(args...);
  return V<decltype(tmp)>(val, tmp);
}

void Solve();

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(20) << fixed;
  Solve();
}

void Solve() {
  li(n, k);
  vli(n, v);
  ll mx = 0;
  vll l(n + 10), r(n + 10);
  l[0] = 0;
  r[0] = 0;
  REP1(i, n) {
    l[i] = l[i - 1] + v[i - 1];
    r[i] = r[i - 1] + v[n - i];
  }

  vvll hs(n + 10, vll(n + 10, 0)), ms(n + 10, vll(n + 10, 0));
  vector<ll> hhs, mms;

  REP1(a, n) {
    hhs.pb(v[a - 1]);
    mms.pb(v[n - a]);
    SORT(hhs);
    SORT(mms);
    REP(b, a) {
      if (b) {
        hs[a][b] = hs[a][b - 1];
        if (hhs[b - 1] < 0) {
          hs[a][b] += hhs[b - 1];
        }
        ms[a][b] = ms[a][b - 1];
        if (mms[b - 1] < 0) {
          ms[a][b] += mms[b - 1];
        }
      }
    }
  }

  REP(i, k + 1) {
    REP(j, k - i + 1) {
      REP(h, k - i - j + 1) {
        REP(m, k - i - j - h + 1) {
          mx = max(mx, l[i] + r[j] - hs[i][h] - ms[j][m]);
        }
      }
    }
  }

  cout << mx;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;

template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
template <class T> using VVV = V<VV<T>>;
template <class S, class T> using P = pair<S, T>;
template <class S, class T, class U> using TP = tuple<S, T, U>;

using ll = long long;
using ull = unsigned long long;
using dbl = double;
using str = string;
using vll = V<ll>;
using vvll = V<vll>;
using vvvll = V<vvll>;
using pl = P<ll, ll>;
using tl = TP<ll, ll, ll>;
using vpl = V<pl>;
using vvpl = V<vpl>;
using vtl = V<tl>;
using vvtl = V<vtl>;
using vs = V<str>;
using vvs = V<vs>;
using vd = V<dbl>;
using vvd = V<vd>;
using qll = queue<ll>;
using qpl = queue<pl>;
using stll = stack<ll>;
using stpl = stack<pl>;
using mapll = map<ll, ll>;
using setll = set<ll>;
using pqll = priority_queue<ll>;

#define int ll
#define fi first
#define se second
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pob pop_back()
#define pf push_front
#define pof pop_front()
#define sz size()
#define bgn begin()
#define en end()
#define asn assign
#define emp empty()
#define fr front()
#define bk back()
#define clr clear()
#define ins insert
#define ers erase
#define res resize
#define tp top()
#define p_q priority_queue
#define inv inverse()

#define FOR(i, a, b) for (ll i = (a); i <= (ll)(b); i++)
#define rFOR(i, a, b) for (ll i = (b); i >= (ll)(a); i--)
#define REP(i, a) FOR((i), 0, (ll)(a)-1)
#define REP0(i, a) FOR((i), 0, (ll)(a))
#define REP1(i, a) FOR((i), 1, (ll)(a))
#define rREP(i, a) rFOR((i), 0, (ll)(a)-1)
#define rREP0(i, a) rFOR((i), 0, (ll)(a))
#define rREP1(i, a) rFOR((i), 1, (ll)(a))
#define ROR(v, i) for (auto &(i) : (v))
#define IOTA(a, n) iota((a).bgn, (a).en, (n))
#define SORT(a) sort((a).bgn, (a).en)
#define rSORT(a) sort((a).rbegin(), (a).rend())
#define UNIQUE(a) (a).erase(unique((a).bgn, (a).en), (a).en)
#define PREVP(a) prev_permutation((a).bgn, (a).en)
#define NEXTP(a) next_permutation((a).bgn, (a).en)
#define BINS(a, b) binary_search((a).bgn, (a).en, (b))
#define LOWB(a, b) (lower_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define UPB(a, b) (upper_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define CNT(a, b) count((a).bgn, (a).en, b)
#define SUM(a) accumulate((a).bgn, (a).en, 0)
#define REV(a) reverse((a).bgn, (a).en)
#define REGS(a, b) regex_search((a), regex(b))
#define REGM(a, b) regex_match((a), regex(b))
#define yn(a) cout << ((a) ? "yes" : "no") << "\n";
#define Yn(a) cout << ((a) ? "Yes" : "No") << "\n";
#define YN(a) cout << ((a) ? "YES" : "NO") << "\n";
#define imp(a) cout << ((a) ? "possible" : "impossible") << "\n";
#define Imp(a) cout << ((a) ? "Possible" : "Impossible") << "\n";
#define IMP(a) cout << ((a) ? "POSSIBLE" : "IMPOSSIBLE") << "\n";
#define fs(a) cout << ((a) ? "second" : "first") << "\n";
#define Fs(a) cout << ((a) ? "Second" : "First") << "\n";
#define FS(a) cout << ((a) ? "SECOND" : "FIRST") << "\n";
#define sak cout << "\n";
#define sas cout << " ";
#define sat cout << "\t";
#define dbg(a) cerr << (#a) << ": " << (a) << "\n";
#define dbgs(...)                                                              \
  dal(#__VA_ARGS__);                                                           \
  dal(__VA_ARGS__);
#define c2l(a) ((ll)(a - 48))
#define a2l(a) ((ll)(a - 97))
#define A2l(a) ((ll)(a - 65))
#define l2c(a) ((char)(a + 48))
#define l2a(a) ((char)(a + 97))
#define l2A(a) ((char)(a + 65))
#define DigN2(a) ((llabs(a) == 0) ? (1) : ((ll)(log2(double(llabs(a)))) + 1))
#define DigN10(a) ((llabs(a) == 0) ? (1) : ((ll)(log10(double(llabs(a)))) + 1))
#define Dig2(a, b) (((a) >> (b)) & 1)
#define Dig10(a, b) (ll)(((a) / ((ll)(pow(10.0, (double)(b))))) % 10)
#define Pow2(a) ((ll)(1) << (a))
#define Pow10(a) ((ll)(pow(10.0, double(a))))
#define LSB(a) ((a) & (-(a)))
#define vin(v)                                                                 \
  ROR((v), (i)) { cin >> (i); };
#define vllin(v, N)                                                            \
  vll(v)((N));                                                                 \
  vin(v);
#define vllin2(a, b, N)                                                        \
  vll(a)(N), (b)(N);                                                           \
  REP(i, N) { cin >> (a)[i] >> (b)[i]; };
#define vsin(v, N)                                                             \
  vs(v)((N));                                                                  \
  vin(v);
#define rdn(a, b) ((a) / (b))
#define rou(a, b)                                                              \
  ((((double(a) / double(b)) - ((a) / (b))) < 0.5) ? ((a) / (b))               \
                                                   : (((a) / (b)) + 1))
#define rup(a, b) ((((a) % (b)) == 0) ? ((a) / (b)) : (((a) / (b)) + 1))
#define min(...) Min(__VA_ARGS__)
#define max(...) Max(__VA_ARGS__)
#define emin(a, ...) ((a) = Min((a), __VA_ARGS__))
#define emax(a, ...) ((a) = Max((a), __VA_ARGS__))
#define egcd(a, ...) ((a) = gcd((a), __VA_ARGS__))
#define elcm(a, ...) ((a) = lcm((a), __VA_ARGS__))
#define powll(a, b) (ll)(pow((double)(a), (double)(b)))
#define Triangle(x1, y1, x2, y2, x3, y3)                                       \
  (((x1) - (x2)) * ((y1) - (y3)) - ((x1) - (x3)) * ((y1) - (y2)))

#define svll SumV<ll>
#define svvll SumV2<ll>

#define li(...)                                                                \
  ll __VA_ARGS__;                                                              \
  Input(__VA_ARGS__);
#define si(...)                                                                \
  str __VA_ARGS__;                                                             \
  Input(__VA_ARGS__);
#define vli(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInput(size, __VA_ARGS__);
#define vsi(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInput(size, __VA_ARGS__);

// const ll MOD = 1e9 + 7;
const ll MOD = 998244353;
// const ll MOD = 924844033;
// const ll MOD = 9007199254740881;
const ll INF = 1LL << 60; // 1.15e18
const double PI = acos(-1.0);
const vll DX = {0, -1, 0, 1, 0, -1, 1, 1, -1};
const vll DY = {0, 0, -1, 0, 1, -1, -1, 1, 1};
const str alp = "abcdefghijklmnopqrstuvwxyz";
const str ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

void Input() {}
template <class Var, class... Args> void Input(Var &var, Args &...args) {
  cin >> var;
  Input(args...);
}

void vInit(ll size) {}
template <class T, class... Args> void vInit(ll size, V<T> &v, Args &...args) {
  v.res(size);
  vInit(size, args...);
}
void vInputNum(ll num) {}
template <class T, class... Args>
void vInputNum(ll num, V<T> &v, Args &...args) {
  cin >> v[num];
  vInputNum(num, args...);
}
void vInput(ll size) {}
template <class... Args> void vInput(ll size, Args &...args) {
  vInit(size, args...);
  REP(i, size) vInputNum(i, args...);
}

template <class S, class T>
ostream &operator<<(ostream &out, const P<S, T> &p) {
  return out << "[" << p.fi << ", " << p.se << "]";
}

template <class T> ostream &operator<<(ostream &out, V<T> &v) {
  if (v.emp)
    return out << "{}";
  else {
    auto itr = v.bgn;
    out << "{" << *itr;
    itr++;
    while (itr != v.en) {
      out << ", " << *itr;
      itr++;
    }
    out << "}";
    return out;
  }
}

template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> &m) {
  if (m.emp)
    return out << "<[]>";
  else {
    auto itr = m.bgn;
    out << "< [" << (itr->fi) << ": " << (itr->se);
    itr++;
    while (itr != m.en) {
      out << "], [" << (itr->fi) << ": " << (itr->se);
      itr++;
    }
    out << "] >";
    return out;
  }
}

template <class T> ostream &operator<<(ostream &out, const set<T> &s) {
  if (s.emp)
    return out << "<>";
  else {
    auto itr = s.bgn;
    out << "<" << *itr;
    itr++;
    while (itr != s.en) {
      out << ", " << *itr;
      itr++;
    }
    out << ">";
    return out;
  }
}

void say() {}
template <class T> void say(T t) { cout << t; }
template <class Head, class... Body> void say(Head head, Body... body) {
  cout << head << " ";
  say(body...);
}
void sal() { cout << "\n"; }
template <class... Args> void sal(Args... args) {
  say(args...);
  cout << "\n";
}

void day() {}
template <class T> void day(T t) { cerr << t; }
template <class Head, class... Body> void day(Head head, Body... body) {
  cerr << head << " ";
  day(body...);
}
void dal() { cerr << "\n"; }
template <class... Args> void dal(Args... args) {
  day(args...);
  cerr << "\n";
}

void salv() {}
template <class T> void salv(V<T> v) {
  if (v.emp)
    sal();
  else {
    auto itr = v.bgn;
    say(*itr);
    itr++;
    while (itr != v.en) {
      sas;
      say(*itr);
      itr++;
    }
    sak;
  }
}
template <class T, class... Args> void salv(V<T> v, Args... args) {
  salv(v);
  salv(args...);
}

void salv2() {}
template <class T> void salv2(V<V<T>> v) {
  if (v.emp)
    sal();
  else {
    ROR(v, i) salv(i);
  }
}
template <class T, class... Args> void salv2(V<V<T>> v, Args... args) {
  salv2(v);
  salv2(args...);
}

template <class Monoid> struct Action {
public:
  Monoid I;
  function<Monoid(Monoid, Monoid)> A;
  Action(Monoid I, function<Monoid(Monoid, Monoid)> A) : I(I), A(A) {}
  Monoid operator()() { return I; }
  Monoid operator()(Monoid x) { return x; }
  Monoid operator()(Monoid l, Monoid r) { return A(l, r); }
  template <class... Args> Monoid operator()(Monoid x, Args... args) {
    Monoid tmp = operator()(args...);
    return A(x, tmp);
  }
};

template <class T> Action<T> ADD = Action<T>(0, [](T l, T r) { return l + r; });
template <>
Action<str> ADD<str> = Action<str>("", [](str l, str r) { return l + r; });
template <class T1, class T2>
Action<P<T1, T2>> ADD<P<T1, T2>> =
    Action<P<T1, T2>>(mp(ADD<T1>.I, ADD<T2>.I), [](P<T1, T2> l, P<T1, T2> r) {
      return mp(l.fi + r.fi, l.se + r.se);
    });

template <class T> Action<T> MUL = Action<T>(1, [](T l, T r) { return l * r; });
template <class T> Action<T> OR = Action<T>(0, [](T l, T r) { return l | r; });
template <class T> Action<T> XOR = Action<T>(0, [](T l, T r) { return l ^ r; });

template <class T>
Action<T> AND = Action<T>(((ll)(1) << 63) - 1, [](T l, T r) { return l & r; });
template <>
Action<bool> AND<bool> =
    Action<bool>(true, [](bool l, bool r) { return l & r; });
template <>
Action<ull> AND<ull> =
    Action<ull>(((ull)(1) << 63) - 1, [](ull l, ull r) { return l & r; });

template <class T>
Action<T> MIN = Action<T>(INF, [](T l, T r) { return (l < r) ? l : r; });
template <class T>
Action<T> MAX = Action<T>(-INF, [](T l, T r) { return (l > r) ? l : r; });

template <class T>
Action<T> GCD = Action<T>(0, [](T l, T r) {
  if (l < r) {
    l ^= r;
    r ^= l;
    l ^= r;
  }
  return (r ? GCD<T>(r, l % r) : l);
});
template <class T>
Action<T> LCM = Action<T>(1, [](T l, T r) { return (l * r) / GCD<T>(l, r); });

template <class Head> Head Min(Head head) { return head; }
template <class Head, class... Body> Head Min(Head head, Body... body) {
  auto tmp = Min(body...);
  return (head < tmp) ? head : tmp;
}

template <class Head> Head Max(Head head) { return head; }
template <class Head, class... Body> auto Max(Head head, Body... body) {
  auto tmp = Max(body...);
  return (head > tmp) ? head : tmp;
}

ll gcd(ll a, ll b) {
  if (a < b) {
    a ^= b;
    b ^= a;
    a ^= b;
  }
  return b ? gcd(b, a % b) : a;
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

ll gcd(ll head) { return head; }
template <class... Body> ll gcd(ll head, Body... body) {
  return gcd(head, gcd(body...));
}

ll lcm(ll head) { return head; }
template <class... Body> ll lcm(ll head, Body... body) {
  return lcm(head, lcm(body...));
}

ll Bset(ll a, ll b, ll c) {
  if (c)
    a |= b;
  else
    a &= ~b;
  return a;
}

struct UFT {

public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  UFT() {}
  UFT(const UFT &uft) {}
  UFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
  }
  ll root(ll x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

struct pUFT {

public:
  ll tsize;
  ll now;
  vll par;
  vll rank;
  vll mtime;
  vvll sizepi;
  vvll sizepv;

  pUFT() {}
  pUFT(const pUFT &puft) {}

  pUFT(ll tsizeget) {
    tsize = tsizeget;
    now = 0;
    par.asn(tsize, -1);
    rank.asn(tsize, 0);
    mtime.asn(tsize, INF);
    sizepi.asn(tsize, {0});
    sizepv.asn(tsize, {1});
  }
  ll root(ll x, ll t) { return (mtime[x] > t) ? x : root(par[x], t); }
  bool same(ll x, ll y, ll t) { return root(x, t) == root(y, t); }
  ll merge(ll x, ll y) {
    now++;
    x = root(x, now);
    y = root(y, now);
    if (x != y) {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        sizepi[y].pb(now);
        sizepv[y].pb(-par[y]);
        par[x] = y;
        mtime[x] = now;
      } else {
        par[x] += par[y];
        sizepi[x].pb(now);
        sizepv[x].pb(-par[x]);
        par[y] = x;
        mtime[y] = now;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
    return now;
  }
  ll size(ll x, ll t) {
    x = root(x, t);
    return sizepv[x][UPB(sizepi[x], t) - 1];
  }
};

struct wUFT {
public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  vll dweight;
  wUFT() {}
  wUFT(const wUFT &wuft) {}
  wUFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
    dweight.asn(tsize, 0);
  }
  ll root(ll x) {
    if (par[x] < 0)
      return x;
    else {
      ll r = root(par[x]);
      dweight[x] += dweight[par[x]];
      return par[x] = r;
    }
  }
  ll weight(ll x) {
    root(x);
    return dweight[x];
  }
  ll diff(ll x, ll y) { return weight(y) - weight(x); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y, ll w) {
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
        dweight[x] = -w;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
        dweight[y] = w;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

template <typename valtype> class SegT {

public:
  ll size;
  vector<valtype> v;

  valtype initv;
  function<valtype(valtype x, valtype y)> calc;

  SegT() {}
  SegT(const SegT &segt) {}

  SegT(ll sizeget, ll modeget = 0) {
    sizeset(sizeget);
    modeset(modeget);
    init();
  }
  SegT(vector<valtype> cpyvec, ll modeget = 0) {
    sizeset(cpyvec.sz);
    modeset(modeget);
    init();
    copy(cpyvec);
  }
  SegT(ll sizeget, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(sizeget);
    initv = initvget;
    calc = calcget;
    init();
  }
  SegT(vector<valtype> cpyvec, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(cpyvec.sz);
    initv = initvget;
    calc = calcget;
    init();
    copy(cpyvec);
  }
  void sizeset(ll rsize) {
    size = DigN2(rsize);
    if (rsize == Pow2(size - 1))
      size--;
    return;
  }
  void modeset(ll mode) {
    switch (mode) {
    case 0:
      initv = 0;
      calc = [](valtype x, valtype y) { return x + y; };
      break;
    case 1:
      initv = INF;
      calc = [](valtype x, valtype y) { return min(x, y); };
      break;
    case 2:
      initv = -INF;
      calc = [](valtype x, valtype y) { return max(x, y); };
      break;
    }
    return;
  }
  void init() { v.asn(Pow2(size + 1) - 1, initv); }
  void copy(vector<valtype> cpyvec) {
    REP(i, min(cpyvec.sz, Pow2(size))) set(i, cpyvec[i]);
  }
  ll i2v(ll i) const {
    if (i < 0 || i >= Pow2(size))
      return -1;
    return Pow2(size) + i - 1;
  }
  ll top(ll i) const {
    if (i == 0)
      return -1;
    return (i - 1) / 2;
  }
  pl bot(ll i) const {
    if (i + 1 >= Pow2(size))
      return mp(-1, -1);
    return mp(2 * i + 1, 2 * i + 2);
  }
  void set(ll i, valtype x) {
    i = i2v(i);
    v[i] = x;
    while (i > 0) {
      i = top(i);
      v[i] = calc(v[bot(i).fi], v[bot(i).se]);
    }
    return;
  }
  void add(ll i, valtype x) {
    set(i, v[i2v(i)] + x);
    return;
  }
  valtype operator[](const ll &i) const { return v[i2v(i)]; }
  //  valtype que(ll a = 0, ll b = Pow2(size) - 1) {
  valtype que(ll a, ll b) {
    if (a == b)
      return v[i2v(a)];
    if (a > b)
      return initv; // swap(a, b);
    valtype ans = initv;
    ll ai = i2v(a);
    ll bi = i2v(b);
    FOR(i, 1, size + 1) {
      if (a > b)
        break;
      if (a % Pow2(i)) {
        ans = calc(ans, v[ai]);
        a += Pow2(i - 1);
        ai = top(ai) + 1;
      } else {
        ai = top(ai);
      }
      if (a > b)
        break;
      if ((b + 1) % Pow2(i)) {
        ans = calc(ans, v[bi]);
        b -= Pow2(i - 1);
        bi = top(bi) - 1;
      } else {
        bi = top(bi);
      }
      if (a > b)
        break;
    }
    return ans;
  }
  valtype que(ll b) { return que(0, b); }
  valtype que() { return que(0, Pow2(size) - 1); }
};

template <typename lentype> class Graph {

public:
  ll size;
  ll mode;
  ll mapmode;
  lentype zlen;
  lentype ilen;
  vector<map<ll, ll>> v2n;
  vvll n2v;
  vector<vector<lentype>> Edge;
  vector<pair<lentype, ll>> Primresult;

  Graph() {}
  Graph(const Graph &graph) {}

  Graph(ll sizeget = 0, ll mapmodeget = 0, ll modeget = 0, lentype zlenget = 0,
        lentype ilenget = INF) {
    size = sizeget;
    mapmode = mapmodeget;
    mode = modeget;
    zlen = zlenget;
    ilen = ilenget;
    init();
  }
  void init() {
    Edge.res(size);
    v2n.res(size);
    n2v.res(size);
    Primresult.asn(size, mp(ilen, -1));
  }
  lentype lenplus(lentype l, lentype r) { return l + r; }
  lentype lenequal(lentype l, lentype r) { return l == r; }
  lentype lenlcr(lentype l, lentype r) { return l < r; }
  ll addV(ll vs) {
    size += vs;
    init();
    return size;
  }
  void caddE(ll x, ll y, lentype c) {
    if (mapmode)
      v2n[x][y] = Edge[x].sz;
    Edge[x].pb(c);
    n2v[x].pb(y);
  }
  void csetE(ll x, ll y, lentype c) {
    if (mapmode)
      Edge[x][v2n[x][y]] = c;
  }
  void cersE(ll x, ll y) {
    if (mapmode) {
      ll n = v2n[x][y];
      Edge[x][n] = ilen;
      n2v[x][n] = -1;
      v2n[x].ers(y);
    }
  }
  void addE(ll x, ll y, lentype c) {
    caddE(x, y, c);
    if (!mode)
      caddE(y, x, c);
  }
  void setE(ll x, ll y, lentype c) {
    csetE(x, y, c);
    if (!mode)
      csetE(y, x, c);
  }
  void ersE(ll x, ll y, lentype c) {
    cersE(x, y, c);
    if (!mode)
      cersE(y, x, c);
  }
  lentype getE(ll x, ll y) {
    if (mapmode) {
      if (v2n[x].count(y)) {
        return Edge[x][v2n[x][y]];
      }
    }
    return ilen;
  }
  ll getVsz(ll x) { return Edge[x].sz; }
  pair<lentype, ll> getV(ll x, ll n) {
    if (n >= getVsz(x))
      return mp(ilen, -1);
    return mp(Edge[x][n], n2v[x][n]);
  }

  vector<pair<lentype, vll>> Dijk(ll x) {
    vector<pair<lentype, vll>> result(size);
    REP(i, size) {
      result[i].fi = ilen;
      result[i].se = {-1};
    }
    vll stat(size, 0);
    pair<lentype, ll> now;
    pair<lentype, ll> nowlv;
    SegT<pair<lentype, ll>> Q(size, mp(ilen, -1),
                              [](pair<lentype, ll> l, pair<lentype, ll> r) {
                                if (l.se == -1)
                                  return r;
                                if (r.se == -1)
                                  return l;
                                return l.fi < r.fi ? l : r;
                              });
    Q.set(x, mp(zlen, x));
    result[x].fi = zlen;
    result[x].se = {-1};
    while (Q.que(0, size - 1).se != -1) {
      now = Q.que(0, size - 1);
      Q.set(now.se, mp(ilen, -1));
      stat[now.se] = 1;
      REP(i, getVsz(now.se)) {
        nowlv = getV(now.se, i);
        if (stat[nowlv.se])
          continue;
        if (Q[nowlv.se].se == -1) {
          result[nowlv.se].fi = lenplus(result[now.se].fi, nowlv.fi);
          result[nowlv.se].se = {now.se};
          Q.set(nowlv.se, mp(result[nowlv.se].fi, nowlv.se));
        } else {
          if (lenlcr(lenplus(result[now.se].fi, nowlv.fi),
                     result[nowlv.se].fi)) {
            result[nowlv.se].fi = lenplus(result[now.se].fi, nowlv.fi);
            result[nowlv.se].se = {now.se};
            Q.set(nowlv.se, mp(result[nowlv.se].fi, nowlv.se));
          } else if (lenequal(lenplus(result[now.se].fi, nowlv.fi),
                              result[nowlv.se].fi)) {
            result[nowlv.se].se.pb(now.se);
          }
        }
      }
    }
    return result;
  }

  lentype Prim(ll x = 0) {
    lentype ans = zlen;
    vll stat(size, 0);
    pair<lentype, ll> now;
    pair<lentype, ll> nowlv;
    SegT<pair<lentype, ll>> Q(size, mp(ilen, -1),
                              [](pair<lentype, ll> l, pair<lentype, ll> r) {
                                if (l.se == -1)
                                  return r;
                                if (r.se == -1)
                                  return l;
                                return l.fi < r.fi ? l : r;
                              });
    Q.set(x, mp(zlen, x));
    Primresult[x] = mp(zlen, -1);
    while (Q.que(0, size - 1).se != -1) {
      now = Q.que(0, size - 1);
      Q.set(now.se, mp(ilen, -1));
      stat[now.se] = 1;
      ans = lenplus(ans, Primresult[now.se].fi);
      REP(i, getVsz(now.se)) {
        nowlv = getV(now.se, i);
        if (stat[nowlv.se])
          continue;
        if (Q[nowlv.se].se == -1) {
          Primresult[nowlv.se] = mp(nowlv.fi, now.se);
          Q.set(nowlv.se, mp(Primresult[nowlv.se].fi, nowlv.se));
        } else {
          if (lenlcr(nowlv.fi, Primresult[nowlv.se].fi)) {
            Primresult[nowlv.se] = mp(nowlv.fi, now.se);
            Q.set(nowlv.se, mp(Primresult[nowlv.se].fi, nowlv.se));
          }
        }
      }
    }
    return ans;
  }
};

/*template <class Type> class DP {

public:

    vector<Type> v;
    Type initv;
    vll size, block;

    DP() {}
    DP(const DP &dp) {}

    template<class... Args> DP(Args... args) {
        block.asn(1, 1);
        Initialize(args...);
    }

    void Initialize(Type initv_) {
        initv = initv_;
        v.asn(block.bk, initv);
    }
    template<class... Args> void Initialize(ll val, Args... args) {
        size.pb(val);
        block.pb(block.bk*val);
        Initialize(args...);
    }



};*/

pl Bezout(ll a, ll b) {
  if (b != 0) {
    pl xy;
    xy = Bezout(b, a % b);
    return mp(xy.se, xy.fi - ((a / b) * xy.se));
  } else {
    return mp(1, 0);
  }
}
pl Bez(ll a, ll b, ll c) {
  pl xy;
  ll x, y, z, gc;
  xy = Bezout(a, b);
  gc = gcd(a, b);
  if (c % gc != 0)
    return mp(-1, -1);
  x = xy.fi * (c / gc);
  y = xy.se * (c / gc);
  if (x < 0)
    z = rup(-x, (b / gc));
  if (x >= 0)
    z = -x / (b / gc);
  x += z * (b / gc);
  y -= z * (a / gc);
  return mp(x, y);
}

ll DigS10(ll n) {
  ll ans = 0;
  while (1) {
    ans += n % 10;
    n /= 10;
    if (!n)
      break;
  }
  return ans;
}

ll isP(ll n) {
  if (n <= 1)
    return 0;
  FOR(i, 2, (ll)sqrt(n) + 1) {
    if (n % i == 0)
      return 0;
  }
  return 1;
}

ll Tot(ll n) {
  if (n <= 0)
    return 0;
  ll ans = n, x = 2;
  while (x * x <= n) {
    if (n % x == 0) {
      ans -= ans / x;
      while (n % x == 0)
        n /= x;
    }
    x++;
  }
  if (n > 1)
    ans -= ans / n;
  return ans;
}

template <class T> struct Sum {
public:
  V<T> v, s;
  ll size;
  Action<T> Add;
  Sum(V<T> v, Action<T> Add = ADD<T>) : v(v), size(v.sz), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(size + 1, Add.I); }
  void Calc() { REP(i, size) s[i + 1] = Add(s[i], v[i]); }
  T operator()(ll x) { return operator()(0, x); }
  T operator()(ll l, ll r) {
    if (l < 0)
      l = 0;
    if (r >= size)
      r = size - 1;
    if (l > r)
      return Add.I;
    return s[r + 1] - s[l]; // for ADD
  }
};
using sumll = Sum<ll>;

template <class T> struct Sum2 {
public:
  V<V<T>> v, s;
  ll RowSize, ColumnSize;
  Action<T> Add;
  Sum2(V<V<T>> v, Action<T> Add = ADD<T>)
      : v(v), RowSize(v.sz), ColumnSize(v.sz ? v[0].sz : 0), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(RowSize + 1, V<T>(ColumnSize, Add.I)); }
  void Calc() {
    REP1(r, RowSize) {
      REP1(c, ColumnSize) {
        s[r][c] =
            v[r - 1][c - 1] + operator()(r, c - 1) + operator()(r - 1, c) -
                                                     operator()(r - 1, c - 1);
      }
    }
  }
  T operator()(ll r, ll c) { return operator()(0, 0, r, c); }
  T operator()(ll r1, ll c1, ll r2, ll c2) {
    if (r1 < 0)
      r1 = 0;
    if (c1 < 0)
      c1 = 0;
    if (r2 >= RowSize)
      r2 = RowSize - 1;
    if (c2 >= ColumnSize)
      c2 = ColumnSize - 1;
    if (r1 > r2)
      return Add.I;
    if (c1 > c2)
      return Add.I;
    return s[r2 + 1][c2 + 1] - s[r2 + 1][c1] - s[r1][c2 + 1] + s[r1][c1];
  }
};
using sum2ll = Sum2<ll>;

template <class T> struct Point2 {
public:
  V<V<T>> v;
  ll h, w;
  Point2() : h(0), w(0) {}
  Point2(ll h, ll w) : h(h), w(w) { asn(h, w); }
  Point2(ll h, ll w, T val) : h(h), w(w) { asn(h, w, val); }
  void assign(ll h, ll w) { v.asn(h, V<T>(w)); }
  void assign(ll h, ll w, ll val) { v.asn(h, V<T>(w, val)); }
  T &operator()(ll h, ll w) { return v[h][w]; }
  T &operator()(pl p) { return v[p.fi][p.se]; }
};
template <class T> using P2 = Point2<T>;

template <ll Mod> struct Modll {
public:
  ll v;
  Modll() : v(0) {}
  Modll(ll _v) { set(_v % Mod + Mod); }
  Modll &set(ll _v) {
    v = (_v < Mod) ? _v : (_v - Mod);
    return *this;
  }
  Modll pow(ll n) const {
    Modll x = *this, ans = 1;
    while (n) {
      if (n & 1)
        ans *= x;
      x *= x;
      n >>= 1;
    }
    return ans;
  }
  Modll inverse() const { return (*this).pow(Mod - 2); }
  Modll operator+(const Modll &m) const { return Modll().set(v + m.v); }
  Modll operator-(const Modll &m) const { return Modll().set(Mod + v - m.v); }
  Modll operator*(const Modll &m) const {
    return Modll().set((ull(v) * m.v) % Mod);
  }
  Modll operator/(const Modll &m) const { return *this * m.inv; }
  Modll &operator+=(const Modll &m) { return *this = *this + m; }
  Modll &operator-=(const Modll &m) { return *this = *this - m; }
  Modll &operator*=(const Modll &m) { return *this = *this * m; }
  Modll &operator/=(const Modll &m) { return *this = *this / m; }
  Modll operator-() const { return Modll(0) - *this; }
  explicit operator bool() const { return v != 0; }
  friend ostream &operator<<(ostream &out, const Modll &m) {
    return out << m.v;
  }
};
using mll = Modll<MOD>;
using vmll = V<mll>;
using vvmll = V<vmll>;
using vvvmll = V<vvmll>;

template <class T> T vmin(V<T> v) {
  T tmp = MIN<T>.I;
  ROR(v, i) emin(tmp, i);
  return tmp;
}
template <class T, class... Args> T vmin(V<T> v, Args... args) {
  T tmp = vmin(args...);
  return min(vmin(v), tmp);
}

template <class T> T vmax(V<T> v) {
  T tmp = MAX<T>.I;
  ROR(v, i) emax(tmp, i);
  return tmp;
}
template <class T, class... Args> T vmax(V<T> v, Args... args) {
  T tmp = vmax(args...);
  return max(vmax(v), tmp);
}

template <class T> T vgcd(V<T> v) {
  T tmp = GCD<T>.I;
  ROR(v, i) egcd(tmp, i);
  return tmp;
}
template <class T, class... Args> T vgcd(V<T> v, Args... args) {
  T tmp = vgcd(args...);
  return gcd(vgcd(v), tmp);
}

template <class T> T vlcm(V<T> v) {
  T tmp = LCM<T>.I;
  ROR(v, i) elcm(tmp, i);
  return tmp;
}
template <class T, class... Args> T vlcm(V<T> v, Args... args) {
  T tmp = vlcm(args...);
  return lcm(vlcm(v), tmp);
}

vmll MFactMemo(2, 1);
vmll MIFactMemo(2, 1);

mll mFact(ll n) {
  if (MFactMemo.sz <= n) {
    ll oldsize = MFactMemo.sz;
    MFactMemo.res(n + 1, 1);
    FOR(i, oldsize, n) MFactMemo[i] = MFactMemo[i - 1] * i;
  }
  return MFactMemo[n];
}
mll miFact(ll n) {
  if (MIFactMemo.sz <= n) {
    ll oldsize = MIFactMemo.sz;
    MIFactMemo.res(n + 1, 1);
    MIFactMemo.bk = mFact(n).inv;
    rFOR(i, oldsize + 1, n) MIFactMemo[i - 1] = MIFactMemo[i] * i;
  }
  return MIFactMemo[n];
}
mll mComb(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return mFact(n) * miFact(k) * miFact(n - k);
}

ll LIS(vll v, ll m = 0) {

  if (v.sz > 0) {
    ll ans = 0;
    vll dp(v.sz, INF);
    FOR(i, 0, v.sz - 1) { dp[m ? UPB(dp, v[i]) : LOWB(dp, v[i])] = v[i]; }
    FOR(i, 0, v.sz - 1) {
      if (dp[i] == INF)
        break;
      ans++;
    }
    return ans;
  } else {
    return 0;
  }
}

void PCmprs(vll &v) {
  if (v.sz == 0)
    return;
  vll vv(v);
  IOTA(vv, 0);
  sort(vv.bgn, vv.en, [&](ll v1, ll v2) { return v[v1] < v[v2]; });
  IOTA(v, 0);
  sort(v.bgn, v.en, [&](ll v1, ll v2) { return vv[v1] < vv[v2]; });
  return;
}

ll BblCnt(vll v) {
  PCmprs(v);
  SegT<ll> b(v.sz, 0);
  ll ans = 0;
  REP(i, v.sz) {
    ans += (i - b.que(0, v[i]));
    b.add(v[i], 1);
  }
  return ans;
}

ll Bsrch(function<bool(ll x)> f, ll mi, ll ma) {
  ll ng = mi - 1, ok = ma, mid;
  while (ok - ng > 1) {
    mid = (ng + ok) / 2;
    (f(mid) ? ok : ng) = mid;
  }
  return ok;
}

template <class T>
V<V<T>> MultiMatrix(V<V<T>> A, V<V<T>> B, Action<T> Mul = MUL<T>,
                    Action<T> Add = ADD<T>) {
  V<V<T>> ans;
  ll ii = A.sz;
  if (!ii)
    return ans;
  ll jj = A[0].sz;
  if (!jj)
    return ans;
  ll jj2 = B.sz;
  if (!jj2)
    return ans;
  if (jj != jj2)
    return ans;
  ll kk = B[0].sz;
  if (!kk)
    return ans;
  ans.asn(ii, V<T>(kk, 0));
  REP(i, ii) {
    REP(k, kk) {
      REP(j, jj) { ans[i][k] = Add(ans[i][k], Mul(A[i][j], B[j][k])); }
    }
  }
  return ans;
}

vvll CombMemo(1000, vll(1000, -1));

ll Comb(ll n, ll k) {
  if ((n < 0) || (k < 0))
    return 0;
  if (CombMemo[n][k] == -1) {
    if (n < k)
      CombMemo[n][k] = 0;
    else {
      if (n == 0)
        CombMemo[n][k] = 1;
      else if (k == 0)
        CombMemo[n][k] = 1;
      else if (n == k)
        CombMemo[n][k] = 1;
      else
        CombMemo[n][k] = Comb(n - 1, k - 1) + Comb(n - 1, k);
    }
  }
  return CombMemo[n][k];
}

template <class T> map<T, ll> Dict(V<T> v) {
  map<T, ll> m;
  if (!v.sz)
    return m;
  SORT(v);
  UNIQUE(v);
  REP(i, v.sz) { m[v[i]] = i; }
  return m;
}

template <class T> vll Cmprs(V<T> v) {
  auto m = Dict(v);
  vll ans(v.sz);
  REP(i, v.sz) { ans[i] = m[v[i]]; }
  return ans;
}

template <class T> auto vecn(T val) { return val; }
template <class... Args> auto vecn(ll val, Args... args) {
  auto tmp = vecn(args...);
  return V<decltype(tmp)>(val, tmp);
}

void Solve();

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(20) << fixed;
  Solve();
}

void Solve() {
  li(n, k);
  vli(n, v);
  ll mx = 0;
  vll l(n + 10), r(n + 10);
  l[0] = 0;
  r[0] = 0;
  REP1(i, n) {
    l[i] = l[i - 1] + v[i - 1];
    r[i] = r[i - 1] + v[n - i];
  }

  vvll hs(n + 10, vll(n + 10, 0)), ms(n + 10, vll(n + 10, 0));
  vector<ll> hhs, mms;

  REP1(a, n) {
    hhs.pb(v[a - 1]);
    mms.pb(v[n - a]);
    SORT(hhs);
    SORT(mms);
    REP(b, a) {
      if (b) {
        hs[a][b] = hs[a][b - 1];
        if (hhs[b - 1] < 0) {
          hs[a][b] += hhs[b - 1];
        }
        ms[a][b] = ms[a][b - 1];
        if (mms[b - 1] < 0) {
          ms[a][b] += mms[b - 1];
        }
      }
    }
  }

  REP(i, min(k, n) + 1) {
    REP(j, min(k, n) - i + 1) {
      REP(h, i + 1) {
        REP(m, j + 1) {
          if (i + j + h + m <= k)
            mx = max(mx, l[i] + r[j] - hs[i][h] - ms[j][m]);
        }
      }
    }
  }

  cout << mx;
}