And here goes another problem on arrays. You are given positive integer len and array a which consists of n integers a1, a2, ..., an. Let's introduce two characteristics for the given array.

  * Let's consider an arbitrary interval of the array with length len, starting in position i. Value <image>, is the modular sum on the chosen interval. In other words, the modular sum is the sum of integers on the chosen interval with length len, taken in its absolute value.
  * Value <image> is the optimal sum of the array. In other words, the optimal sum of an array is the maximum of all modular sums on various intervals of array with length len. 



Your task is to calculate the optimal sum of the given array a. However, before you do the calculations, you are allowed to produce no more than k consecutive operations of the following form with this array: one operation means taking an arbitrary number from array ai and multiply it by -1. In other words, no more than k times you are allowed to take an arbitrary number ai from the array and replace it with  - ai. Each number of the array is allowed to choose an arbitrary number of times.

Your task is to calculate the maximum possible optimal sum of the array after at most k operations described above are completed.

Input

The first line contains two integers n, len (1 ≤ len ≤ n ≤ 105) — the number of elements in the array and the length of the chosen subinterval of the array, correspondingly. 

The second line contains a sequence consisting of n integers a1, a2, ..., an (|ai| ≤ 109) — the original array. 

The third line contains a single integer k (0 ≤ k ≤ n) — the maximum allowed number of operations. 

All numbers in lines are separated by a single space.

Output

In a single line print the maximum possible optimal sum after no more than k acceptable operations are fulfilled. 

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Examples

Input

5 3
0 -2 3 -5 1
2


Output

10


Input

5 2
1 -3 -10 4 1
3


Output

14


Input

3 3
-2 -5 4
1


Output

11
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-9;
const int BUFFER_SIZE = 1 << 20;
const int INF = 1 << 30;
const long long LINF = 1ll << 60;
char BUFFER[BUFFER_SIZE];
int gi() {
  int x;
  scanf("%d", &x);
  return x;
}
double gd() {
  double x;
  scanf("%lf", &x);
  return x;
}
vector<int> gvi(int n) {
  vector<int> a;
  while (n--) a.push_back(gi());
  return a;
}
string gs() {
  scanf("%s", BUFFER);
  return string(BUFFER);
}
istringstream buff() { return istringstream(string(BUFFER)); }
template <class T>
struct forArray {
  T* a;
  int n;
  forArray(T* a, int n) : a(a), n(n) {}
};
template <class A, class B>
ostream& operator<<(ostream& os, const pair<A, B>& d);
template <class T>
ostream& operator<<(ostream& os, const vector<T>& d);
template <class T>
ostream& operator<<(ostream& os, const queue<T>& d);
template <class T>
ostream& operator<<(ostream& os, const stack<T>& d);
template <class T>
ostream& operator<<(ostream& os, const set<T>& d);
template <class T>
ostream& operator<<(ostream& os, const multiset<T>& d);
template <class T>
ostream& operator<<(ostream& os, const unordered_set<T>& d);
template <class A, class B>
ostream& operator<<(ostream& os, const map<A, B>& d);
template <class A, class B>
ostream& operator<<(ostream& os, const multimap<A, B>& d);
template <class A, class B>
ostream& operator<<(ostream& os, const unordered_map<A, B>& d);
template <class T>
ostream& operator<<(ostream& os, const vector<T>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class T>
ostream& operator<<(ostream& os, const queue<T>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class T>
ostream& operator<<(ostream& os, const stack<T>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class T>
ostream& operator<<(ostream& os, const set<T>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class T>
ostream& operator<<(ostream& os, const multiset<T>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class T>
ostream& operator<<(ostream& os, const unordered_set<T>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class A, class B>
ostream& operator<<(ostream& os, const map<A, B>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class A, class B>
ostream& operator<<(ostream& os, const multimap<A, B>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class A, class B>
ostream& operator<<(ostream& os, const unordered_map<A, B>& d) {
  os << "[";
  int f = 0;
  for (auto x : d) {
    if (f) os << ",";
    f = 1;
    os << x;
  }
  return os << "]";
};
template <class T>
ostream& operator<<(ostream& os, const forArray<T>& d) {
  os << "[";
  for (int i = 0; i < d.n; ++i) {
    if (i) os << ",";
    os << d.a[i];
  }
  return os << "]";
}
template <class A, class B>
ostream& operator<<(ostream& os, const pair<A, B>& d) {
  return os << "[" << d.first << ", " << d.second << "]";
}
multiset<long long> mins;
multiset<long long> mins2;
long long minsSum = 0;
multiset<long long> maxs;
multiset<long long> maxs2;
long long maxsSum = 0;
int K;
void fadd(int x) {
  if (x < 0) {
    minsSum += x;
    mins.insert(x);
    while (mins.size() > K) {
      int x = *--mins.end();
      minsSum -= x;
      mins.erase(--mins.end());
      mins2.insert(x);
    }
  } else {
    maxsSum += x;
    maxs.insert(x);
    while (maxs.size() > K) {
      int x = *maxs.begin();
      maxsSum -= x;
      maxs.erase(maxs.begin());
      maxs2.insert(x);
    }
  }
}
void fdel(int x) {
  if (x < 0) {
    if (mins2.find(x) != mins2.end()) {
      mins2.erase(mins2.find(x));
    } else {
      minsSum -= x;
      mins.erase(mins.find(x));
      while (mins.size() < K && mins2.size()) {
        int x = *mins2.begin();
        minsSum += x;
        mins2.erase(mins2.begin());
        mins.insert(x);
      }
    }
  } else {
    if (maxs2.find(x) != maxs2.end()) {
      maxs2.erase(maxs2.find(x));
    } else {
      maxsSum -= x;
      maxs.erase(maxs.find(x));
      while (maxs.size() < K && maxs2.size()) {
        int x = *(--maxs2.end());
        maxsSum += x;
        maxs2.erase(--maxs2.end());
        maxs.insert(x);
      }
    }
  }
}
int main() {
  int n = gi();
  int L = gi();
  vector<int> a = gvi(n);
  K = gi();
  long long S = 0;
  for (int i = 0; i < L - 1; ++i) {
    fadd(a[i]);
    S += a[i];
  }
  long long best = -LINF;
  for (int i = L - 1; i < n; ++i) {
    fadd(a[i]);
    S += a[i];
    long long v1 = S - 2ll * minsSum;
    long long v2 = S - 2ll * maxsSum;
    best = max(best, max(abs(v1), abs(v2)));
    S -= a[i - L + 1];
    fdel(a[i - L + 1]);
  }
  cout << best << endl;
  return 0;
}
