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;
const int maxn = 1e5 + 10;
long long a[maxn], b[maxn], f[maxn];
int main() {
  int n, m, q;
  while (cin >> n >> m >> q) {
    long long num = 1;
    long long sum = 0;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      sum += a[i] * num;
      num = -num;
    }
    for (int i = 1; i <= m; i++) cin >> b[i];
    num = 1;
    f[0] = 0;
    for (int i = 1; i <= n; i++) {
      f[0] += num * b[i];
      num = -num;
    }
    if (n & 1)
      num = 1;
    else
      num = -1;
    for (int i = 1; i <= m - n; i++) f[i] = -f[i - 1] + b[i] + b[i + n] * num;
    sort(f, f + m - n + 1);
    long long ans;
    int pos = lower_bound(f, f + m - n + 1, sum) - f;
    if (pos < m - n + 1) {
      ans = abs(f[pos] - sum);
      if (pos > 0) ans = min(ans, abs(f[pos - 1] - sum));
    } else
      ans = abs(f[pos - 1] - sum);
    cout << ans << endl;
    int l, r;
    long long x;
    while (q--) {
      cin >> l >> r >> x;
      r = r - l + 1;
      if (r & 1) {
        if (l & 1)
          sum += x;
        else
          sum -= x;
        pos = lower_bound(f, f + m - n + 1, sum) - f;
        if (pos < m - n + 1) {
          ans = abs(f[pos] - sum);
          if (pos > 0) ans = min(ans, abs(f[pos - 1] - sum));
        } else
          ans = abs(f[pos - 1] - sum);
      }
      cout << ans << endl;
    }
  }
  return 0;
}
