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.util.*;
import java.io.*;
import java.lang.Math.*;

public class MainA
{

	static int mod = (int) 1e9 + 7;

	public static void main(String[] args) throws java.lang.Exception
	{
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n=in.nextInt();
		int m=in.nextInt();
		int q=in.nextInt();
		long a[]=new long[n];
		long b[]=new long[m];
		long sum_a=0;
		for(int i=0;i<n;i++)
		{
			a[i]=in.nextLong();
			if(i%2==0)
			{
				sum_a+=a[i];
			}
			else
				sum_a-=a[i];
		}
		//out.println(sum_a);
		long sumb[]=new long[m-n+1] ;
		for(int i=0;i<m;i++)
		{
			b[i]=in.nextLong();
		}
		for(int i=0;i<n;i++)
		{
			if(i%2==0)sumb[0]-=b[i];
			else sumb[0]+=b[i];
		}
	
		int k=1;
		for(int i=n;i<m;i++,k++)
		{
			
			sumb[k]=sumb[k-1]+b[i-n];	
			sumb[k]=-(sumb[k]);
			if(n%2==0)
			{
				sumb[k]+=b[i];
			}
			else sumb[k]-=b[i];
			
		}
		Arrays.sort(sumb);
		int ind=biSe(sumb,-sum_a,m-n+1);
		long min=Long.MAX_VALUE;
		if(ind+1<=m-n)
		{
			if(Math.abs(sumb[ind+1]+sum_a)<min)min=Math.abs(sumb[ind+1]+sum_a);
		}
		if(ind>=0)
		{
			if(Math.abs(sumb[ind]+sum_a)<min)min=Math.abs(sumb[ind]+sum_a);
		}
		if(ind-1>=0)
		{
			if(Math.abs(sumb[ind-1]+sum_a)<min)min=Math.abs(sumb[ind-1]+sum_a);
		}
		out.println(min);
		long prev=min;
		while(q-->0)
		{
			int l=in.nextInt();
			int r=in.nextInt();
			int x=in.nextInt();
			if((r-l+1)%2==0)
			{
				out.println(prev);
			}
			else
			{
				if(l%2==1)
				{
					sum_a+=x;
				}
				else sum_a-=x;
				ind=biSe(sumb,-sum_a,m-n+1);
				min=Long.MAX_VALUE;
				if(ind+1<=m-n)
				{
					if(Math.abs(sumb[ind+1]+sum_a)<min)min=Math.abs(sumb[ind+1]+sum_a);
				}
				if(ind>=0)
				{
					if(Math.abs(sumb[ind]+sum_a)<min)min=Math.abs(sumb[ind]+sum_a);
				}
				if(ind-1>=0)
				{
					if(Math.abs(sumb[ind-1]+sum_a)<min)min=Math.abs(sumb[ind-1]+sum_a);
				}
				prev=min;
				out.println(min);
			}
		}
		out.close();
	}

	public static int biSe(long sum[],long x,int n)
	{
		int l=0;
		int r=n-1;
		int ret=-1;
		while(l<=r)
		{
			int mid=(l+r)/2;
			if(sum[mid]==x)return mid;
			if(sum[mid]<x)
			{
				ret=mid;
				l=mid+1;
			}
			else
			{
				r=mid-1;
			}		
		}
		return ret;
	}
	static class Pairs implements Comparable<Pairs>
	{
		int x;
		int y;
		int z;
		
		Pairs(int a, int b,int c)
		{
			x = a;
			y = b;
			z=c;
		}

		@Override
		public int compareTo(Pairs o)
		{
			// TODO Auto-generated method stub
			if (y == o.y)
			{	
				if(z!=o.z)
				return Integer.compare(-z, -o.z);
				else
				return Integer.compare(x,o.x);	
			}	
			else
				return Integer.compare(y, o.y);
		}

	}

	public static void debug(Object... o) 
	{
		System.out.println(Arrays.deepToString(o));
	}

	public static boolean isPal(String s) 
	{
		for (int i = 0, j = s.length() - 1; i <= j; i++, j--)
		{
			if (s.charAt(i) != s.charAt(j))
				return false;
		}
		return true;
	}

	public static String rev(String s)
	{
		StringBuilder sb = new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}

	public static long gcd(long x, long y)
	{
		if (y == 0)
			return x;
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static int gcd(int x, int y)
	{
		if(y==0)
			return x;
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static long gcdExtended(long a, long b, long[] x) 
	{

		if (a == 0) 
		{
			x[0] = 0;
			x[1] = 1;
			return b;
		}
		long[] y = new long[2];
		long gcd = gcdExtended(b % a, a, y);

		x[0] = y[1] - (b / a) * y[0];
		x[1] = y[0];

		return gcd;
	}

	
	

	public static long max(long a, long b) 
	{
		if (a > b)
			return a;
		else
			return b;
	}

	public static long min(long a, long b)
	{
		if (a > b)
			return b;
		else
			return a;
	}

	public static long[][] mul(long a[][], long b[][])
	{
		long c[][] = new long[2][2];
		c[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0];
		c[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1];
		c[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0];
		c[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1];

		return c;
	}

	public static long[][] pow(long n[][], long p, long m)
	{
		long result[][] = new long[2][2];
		result[0][0] = 1;
		result[0][1] = 0;
		result[1][0] = 0;
		result[1][1] = 1;

		if (p == 0)
			return result;
		if (p == 1)
			return n;
		while (p != 0)
		{
			if (p % 2 == 1)
				result = mul(result, n);
			//System.out.println(result[0][0]);
			for (int i = 0; i < 2; i++)
			{
				for (int j = 0; j < 2; j++)
				{
					if (result[i][j] >= m)
						result[i][j] %= m;
				}
			}

			p >>= 1;
			n = mul(n, n);
			// System.out.println(1+" "+n[0][0]+" "+n[0][1]+" "+n[1][0]+" "+n[1][1]);
			for (int i = 0; i < 2; i++) 
			{
				for (int j = 0; j < 2; j++)
				{
					if (n[i][j] >= m)
						n[i][j] %= m;
				}
			}
		}
		return result;
	}
	public static long pow(long n,long p, long m)
	{
		long result=1;
		if(p==0)return 1;
		if(p==1)return n%m;
		while(p!=0)
		{
			if(p%2==1)result=(result*n)%m;
			p >>=1;
			n=(n*n)%m;
		}
		return result;
	}
	public static long pow(long n, long p) 
	{
		long result = 1;
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		while (p != 0)
		{
			if (p % 2 == 1)
				result *= n;
			p >>= 1;
			n *= n;
		}
		return result;
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

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

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

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

		public int[] nextIntArray(int n)
		{
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
			{
				a[i] = nextInt();
			}
			return a;
		}

		public long[] nextLongArray(int n)
		{
			long a[] = new long[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextInt();
			}
			return a;
		}

		public String readString()
		{
			int c = snext();
			while (isSpaceChar(c))
			{
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = snext();
			} 
			while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine()
		{
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = snext();
			}
			while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c)
		{
			return c == '\n' || c == '\r' || c == -1;
		}

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