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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni();
		int m = ni();
		int[] a = na(n-1);
		int[][] b = new int[n][];
		for(int i = 0;i < n;i++){
			b[i] = na(m);
		}
		long[][] imos = new long[n+2][n+2];
		int[] row = new int[n];
		int[] pw = new int[n];
		int[] nw = new int[n];
		for(int i = 0;i < m;i++){
			for(int j = 0;j < n;j++)row[j] = b[j][i];
			enumPrevWall(row, pw);
			enumNextWall(row, nw);
			for(int j = 0;j < n;j++){
				// [pw[j]+1,j]*[j,nw[j]-1]
				add(imos, pw[j]+1, j, j, nw[j]-1, row[j]);
			}
		}
		for(int i = 0;i <= n;i++){
			for(int j = 0;j <= n;j++){
				imos[i][j+1] += imos[i][j];
			}
		}
		for(int i = 0;i <= n;i++){
			for(int j = 0;j <= n;j++){
				imos[j+1][i] += imos[j][i];
			}
		}
		
		long[] xs = new long[n];
		for(int i = 0;i < n-1;i++){
			xs[i+1] = xs[i] + a[i];
		}
		
		long max = 0;
		for(int i = 0;i < n;i++){
			for(int j = i;j < n;j++){
				max = Math.max(max,-(xs[j]-xs[i])+imos[i][j]); 
			}
		}
		out.println(max);
	}
	
	static void add(long[][] imos, int r1, int r2, int c1, int c2, long v)
	{
		imos[r1][c1] += v;
		imos[r1][c2+1] -= v;
		imos[r2+1][c1] -= v;
		imos[r2+1][c2+1] += v;
	}
	
	public static int[] enumPrevWall(int[] a, int[] L)
	{
		int n = a.length;
		for(int i = 0;i < n;i++){
			L[i] = i-1;
			while(L[i] >= 0 && a[L[i]] < a[i])L[i] = L[L[i]];
		}
		return L;
	}
	
	public static int[] enumNextWall(int[] a, int[] L)
	{
		int n = a.length;
		for(int i = n-1;i >= 0;i--){
			L[i] = i+1;
			while(L[i] < n && a[L[i]] <= a[i])L[i] = L[L[i]];
		}
		return L;
	}
	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
