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.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt(), q = in.nextInt();
            long a[] = in.parseLong1D(n);
            long b[] = in.parseLong1D(m);
            long alternateSumA = 0;
            for (int i = 0; i < a.length; i++) {
                alternateSumA += i % 2 == 0 ? a[i] : -a[i];
            }
            long sumB[] = new long[m - n + 1];
            long firstPos[] = new long[m];
            long firstNeg[] = new long[m];
            firstPos[0] = b[0];
            firstNeg[0] = -b[0];
            for (int i = 1; i < b.length; i++) {
                firstPos[i] = firstPos[i - 1] + (i % 2 == 0 ? b[i] : -b[i]);
                firstNeg[i] = firstNeg[i - 1] + (i % 2 == 0 ? -b[i] : b[i]);
            }
            for (int i = 0; i < sumB.length; i++) {
                if (i % 2 == 0) {
                    sumB[i] = firstPos[i + n - 1] - (i - 1 >= 0 ? firstPos[i - 1] : 0);
                } else {
                    sumB[i] = firstNeg[i + n - 1] - (i - 1 >= 0 ? firstNeg[i - 1] : 0);
                }
            }

            ArrayList<Long> neg = new ArrayList<>();
            ArrayList<Long> pos = new ArrayList<>();
            for (long v : sumB) {
                if (v < 0) {
                    neg.add(-v);
                } else {
                    pos.add(v);
                }
            }
            Collections.sort(neg);
            Collections.sort(pos);
            q++;
            while (q-- != 0) {
                int indexNeg = Collections.binarySearch(neg, Math.abs(alternateSumA));
                long ans = Long.MAX_VALUE;
                if (indexNeg < 0) {
                    indexNeg = -indexNeg - 1;
                }
                for (int i = Math.max(0, indexNeg - 3); i <= Math.min(neg.size() - 1, indexNeg + 3); i++) {
                    ans = Math.min(Math.abs(alternateSumA + neg.get(i)), ans);
                }
                int indexPos = Collections.binarySearch(pos, Math.abs(alternateSumA));
                if (indexPos < 0) {
                    indexPos = -indexPos - 1;
                }
                for (int i = Math.max(0, indexPos - 3); i <= Math.min(pos.size() - 1, indexPos + 3); i++) {
                    ans = Math.min(Math.abs(alternateSumA - pos.get(i)), ans);
                }
                if (pos.size() > 0) {
                    ans = Math.min(Math.abs(alternateSumA - pos.get(0)), ans);
                    ans = Math.min(Math.abs(alternateSumA - pos.get(pos.size() - 1)), ans);
                }

                if (neg.size() > 0) {
                    ans = Math.min(Math.abs(alternateSumA + neg.get(0)), ans);
                    ans = Math.min(Math.abs(alternateSumA + neg.get(neg.size() - 1)), ans);
                }
                out.println(ans);
                if (q == 0) {
                    break;
                }
                int st = in.nextInt() - 1;
                int end = in.nextInt() - 1;
                long value = in.nextLong();
                if (st % 2 == 1 && end % 2 == 1) {
                    alternateSumA += -value;
                } else if (st % 2 == 0 && end % 2 == 0) {
                    alternateSumA += value;
                }
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int nextInt() {
            return readInt();
        }

        public long nextLong() {
            return readLong();
        }

        public long[] parseLong1D(int n) {
            long r[] = new long[n];
            for (int i = 0; i < n; i++) {
                r[i] = readLong();
            }
            return r;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

