There are N barbecue restaurants along a street. The restaurants are numbered 1 through N from west to east, and the distance between restaurant i and restaurant i+1 is A_i.

Joisino has M tickets, numbered 1 through M. Every barbecue restaurant offers barbecue meals in exchange for these tickets. Restaurant i offers a meal of deliciousness B_{i,j} in exchange for ticket j. Each ticket can only be used once, but any number of tickets can be used at a restaurant.

Joisino wants to have M barbecue meals by starting from a restaurant of her choice, then repeatedly traveling to another barbecue restaurant and using unused tickets at the restaurant at her current location. Her eventual happiness is calculated by the following formula: "(The total deliciousness of the meals eaten) - (The total distance traveled)". Find her maximum possible eventual happiness.

Constraints

* All input values are integers.
* 2≤N≤5×10^3
* 1≤M≤200
* 1≤A_i≤10^9
* 1≤B_{i,j}≤10^9

Input

The input is given from Standard Input in the following format:


N M
A_1 A_2 ... A_{N-1}
B_{1,1} B_{1,2} ... B_{1,M}
B_{2,1} B_{2,2} ... B_{2,M}
:
B_{N,1} B_{N,2} ... B_{N,M}


Output

Print Joisino's maximum possible eventual happiness.

Examples

Input

3 4
1 4
2 2 5 1
1 3 3 2
2 2 5 1


Output

11


Input

5 3
1 2 3 4
10 1 1
1 1 1
1 10 1
1 1 1
1 1 10


Output

20
import java.io.*;
import java.util.*;

public class Main {
	static final StdIn in = new StdIn();
	static final PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		int n=in.nextInt(), m=in.nextInt();
		long[] a=in.readLongArray(n-1, 0);
		long[][] b = new long[n][m];
		for(int i=0; i<n; ++i)
			b[i]=in.readLongArray(m, 0);
		SegTree st = new SegTree(n);
		long[] ini = new long[n], mx1 = new long[m];
		long ps=0, ans=0;
		for(int i=0; i<n; ++i) {
			for(int j=0; j<m; ++j)
				ini[i]+=mx1[j]=Math.max(b[i][j], mx1[j]);
			ini[i]-=ps;
			if(i<n-1)
				ps+=a[i];
		}
		st.build(ini);
		int[][] nxt = new int[n][m];
		for(int i=n-1; i>=0; --i) {
			for(int j=0; j<m; ++j) {
				nxt[i][j]=i+1;
				while(nxt[i][j]<n&&b[nxt[i][j]][j]<b[i][j])
					nxt[i][j]=nxt[nxt[i][j]][j];
			}
		}
		ps=0;
		for(int i=0; i<n; ++i) {
			ans=Math.max(st.get(i, n-1)+ps, ans);
			for(int j=0; j<m; ++j) {
				st.add(i, nxt[i][j]-1, -b[i][j]);
				for(int k=i+1; k<n&&b[k][j]<b[i][j]; k=nxt[k][j])
					st.add(k, nxt[k][j]-1, b[k][j]);
			}
			if(i<n-1)
				ps+=a[i];
		}
		out.println(ans);
		out.close();
	}
	
	static class SegTree {
		int n, l1, r1;
		long v;
		long[] a, lazy;
		SegTree(int n) {
			this.n=n;
			a = new long[4*n];
			lazy = new long[4*n];
		}
		void build(long[] b) {
			build2(1, 0, n-1, b);
		}
		private void build2(int i, int l2, int r2, long[] b) {
			if(l2<r2) {
				int mid=(l2+r2)/2;
				build2(2*i, l2, mid, b);
				build2(2*i+1, mid+1, r2, b);
				a[i]=Math.max(a[2*i], a[2*i+1]);
			} else
				a[i]=b[l2];
		}
		void add(int l, int r, long x) {
			l1=l;
			r1=r;
			v=x;
			add2(1, 0, n-1);
		}
		private void add2(int i, int l2, int r2) {
			if(l1<=l2&&r2<=r1) {
				a[i]+=v;
				if(l2<r2) {
					lazy[2*i]+=v;
					lazy[2*i+1]+=v;
				}
			} else {
				int mid=(l2+r2)/2;
				push(i*2, l2, mid);
				push(i*2+1, mid+1, r2);
				if(l1<=mid)
					add2(i*2, l2, mid);
				if(mid<r1)
					add2(i*2+1, mid+1, r2);
				a[i]=Math.max(a[i*2], a[i*2+1]);
			}
		}
		void push(int i, int l, int r) {
			a[i]+=lazy[i];
			if(l<r) {
				lazy[2*i]+=lazy[i];
				lazy[2*i+1]+=lazy[i];
			}
			lazy[i]=0;
		}
		long get(int l, int r) {
			l1=l;
			r1=r;
			return get2(1, 0, n-1);
		}
		private long get2(int i, int l2, int r2) {
			push(i, l2, r2);
			if(l1<=l2&&r2<=r1)
				return a[i];
			else {
				int mid=(l2+r2)/2;
				long res=Long.MIN_VALUE;
				if(l1<=mid)
					res = Math.max(get2(2*i, l2, mid), res);
				if(mid<r1)
					res = Math.max(get2(2*i+1, mid+1, r2), res);
				return res;
			}
		}
	}
	
	static class StdIn {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;
		public StdIn() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		public StdIn(InputStream in) {
			try{
				din = new DataInputStream(in);
			} catch(Exception e) {
				throw new RuntimeException();
			}
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		public String next() {
			int c;
			while((c=read())!=-1&&(c==' '||c=='\n'||c=='\r'));
			StringBuilder s = new StringBuilder();
			while (c != -1)
			{
				if (c == ' ' || c == '\n'||c=='\r')
					break;
				s.append((char)c);
				c=read();
			}
			return s.toString();
		}
		public String nextLine() {
			int c;
			while((c=read())!=-1&&(c==' '||c=='\n'||c=='\r'));
			StringBuilder s = new StringBuilder();
			while (c != -1)
			{
				if (c == '\n'||c=='\r')
					break;
				s.append((char)c);
				c = read();
			}
			return s.toString();
		}
		public int nextInt() {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}
		public int[] readIntArray(int n, int os) {
			int[] ar = new int[n];
			for(int i=0; i<n; ++i)
				ar[i]=nextInt()+os;
			return ar;
		}
		public long nextLong() {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		public long[] readLongArray(int n, long os) {
			long[] ar = new long[n];
			for(int i=0; i<n; ++i)
				ar[i]=nextLong()+os;
			return ar;
		}
		public double nextDouble() {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}
		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
		private byte read() {
			try{
				if (bufferPointer == bytesRead)
					fillBuffer();
				return buffer[bufferPointer++];
			} catch(IOException e) {
				throw new RuntimeException();
			}
		}
		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
}