Dr. Evil is interested in math and functions, so he gave Mahmoud and Ehab array a of length n and array b of length m. He introduced a function f(j) which is defined for integers j, which satisfy 0 ≤ j ≤ m - n. Suppose, ci = ai - bi + j. Then f(j) = |c1 - c2 + c3 - c4... cn|. More formally, <image>. 

Dr. Evil wants Mahmoud and Ehab to calculate the minimum value of this function over all valid j. They found it a bit easy, so Dr. Evil made their task harder. He will give them q update queries. During each update they should add an integer xi to all elements in a in range [li;ri] i.e. they should add xi to ali, ali + 1, ... , ari and then they should calculate the minimum value of f(j) for all valid j.

Please help Mahmoud and Ehab.

Input

The first line contains three integers n, m and q (1 ≤ n ≤ m ≤ 105, 1 ≤ q ≤ 105) — number of elements in a, number of elements in b and number of queries, respectively.

The second line contains n integers a1, a2, ..., an. ( - 109 ≤ ai ≤ 109) — elements of a.

The third line contains m integers b1, b2, ..., bm. ( - 109 ≤ bi ≤ 109) — elements of b.

Then q lines follow describing the queries. Each of them contains three integers li ri xi (1 ≤ li ≤ ri ≤ n,  - 109 ≤ x ≤ 109) — range to be updated and added value.

Output

The first line should contain the minimum value of the function f before any update.

Then output q lines, the i-th of them should contain the minimum value of the function f after performing the i-th update .

Example

Input

5 6 3
1 2 3 4 5
1 2 3 4 5 6
1 1 10
1 1 -9
1 5 -1


Output

0
9
0
0

Note

For the first example before any updates it's optimal to choose j = 0, f(0) = |(1 - 1) - (2 - 2) + (3 - 3) - (4 - 4) + (5 - 5)| = |0| = 0.

After the first update a becomes {11, 2, 3, 4, 5} and it's optimal to choose j = 1, f(1) = |(11 - 2) - (2 - 3) + (3 - 4) - (4 - 5) + (5 - 6) = |9| = 9.

After the second update a becomes {2, 2, 3, 4, 5} and it's optimal to choose j = 1, f(1) = |(2 - 2) - (2 - 3) + (3 - 4) - (4 - 5) + (5 - 6)| = |0| = 0.

After the third update a becomes {1, 1, 2, 3, 4} and it's optimal to choose j = 0, f(0) = |(1 - 1) - (1 - 2) + (2 - 3) - (3 - 4) + (4 - 5)| = |0| = 0.
#include <bits/stdc++.h>
using namespace std;
int N, M, Q;
vector<int> A, B;
set<long long> st;
inline int sign(int val) { return val & 1 ? -1 : 1; }
long long solve(long long val) {
  auto it = st.lower_bound(val);
  if (it == st.end()) --it;
  long long res = abs(*it - val);
  if (it != st.begin()) --it;
  return min(res, abs(*it - val));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> N >> M >> Q;
  A.resize(N), B.resize(M);
  long long c = 0;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    c += A[i] * sign(i);
  }
  long long curr = 0;
  for (int i = 0; i < N; i++) {
    cin >> B[i];
    curr += B[i] * sign(i + 1);
  }
  st.insert(curr);
  for (int i = N; i < M; i++) {
    cin >> B[i];
    curr += B[i - N];
    curr *= -1;
    curr += B[i] * sign(N);
    st.insert(curr);
  }
  cout << solve(-c) << "\n";
  while (Q--) {
    int l, r, v;
    cin >> l >> r >> v;
    if ((r - l + 1) & 1) {
      if (l & 1)
        c += v;
      else
        c -= v;
    }
    cout << solve(-c) << "\n";
  }
  return 0;
}
