Problem: Polycarp is an introvert person. In fact he is so much of an introvert that he plays "Monsters and Potions" board game alone. The board of the game is a row of n cells. The cells are numbered from 1 to n from left to right. There are three types of cells: a cell containing a single monster, a cell containing a single potion or a blank cell (it contains neither a monster nor a potion).

Polycarp has m tokens representing heroes fighting monsters, which are initially located in the blank cells s_1, s_2, ..., s_m. Polycarp's task is to choose a single cell (rally point) and one by one move all the heroes into this cell. A rally point can be a cell of any of three types.

After Policarp selects a rally point, he picks a hero and orders him to move directly to the point. Once that hero reaches the point, Polycarp picks another hero and orders him also to go to the point. And so forth, until all the heroes reach the rally point cell. While going to the point, a hero can not deviate from the direct route or take a step back. A hero just moves cell by cell in the direction of the point until he reaches it. It is possible that multiple heroes are simultaneously in the same cell.

Initially the i-th hero has h_i hit points (HP). Monsters also have HP, different monsters might have different HP. And potions also have HP, different potions might have different HP.

If a hero steps into a cell which is blank (i.e. doesn't contain a monster/potion), hero's HP does not change.

If a hero steps into a cell containing a monster, then the hero and the monster fight. If monster's HP is strictly higher than hero's HP, then the monster wins and Polycarp loses the whole game. If hero's HP is greater or equal to monster's HP, then the hero wins and monster's HP is subtracted from hero's HP. I.e. the hero survives if his HP drops to zero, but dies (and Polycarp looses) if his HP becomes negative due to a fight. If a hero wins a fight with a monster, then the monster disappears, and the cell becomes blank.

If a hero steps into a cell containing a potion, then the hero drinks the potion immediately. As a result, potion's HP is added to hero's HP, the potion disappears, and the cell becomes blank.

Obviously, Polycarp wants to win the game. It means that he must choose such rally point and the order in which heroes move, that every hero reaches the rally point and survives. I.e. Polycarp loses if a hero reaches rally point but is killed by a monster at the same time. Polycarp can use any of n cells as a rally point — initially it can contain a monster, a potion, or be a blank cell with or without a hero in it.

Help Polycarp write a program to choose a rally point and the order in which heroes move.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 100; 1 ≤ m ≤ n) — length of the game board and the number of heroes on it.

The following m lines describe heroes. Each line contains two integers s_i and h_i (1 ≤ s_i ≤ n; 1 ≤ h_i ≤ 10^6), where s_i is the initial position and h_i is the initial HP of the i-th hero. It is guaranteed that each cell s_i is blank. It is also guaranteed that all s_i are different. 

The following line contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_j ≤ 10^6), where a_j describes the i-th cell of the game board:

  * a_j=0 means that the i-th cell is blank, 
  * a_j<0 means that the i-th cell contains monster with positive HP of -a_j, 
  * a_j>0 means that the i-th cell contains potion with a_j HP. 

Output

On the first line of the output print the index of the rally point cell.

On the second line print m integers — the order in which heroes should move to the rally point. Heroes are numbered from 1 to m in the order they are given in the input.

If there are multiple solutions, print any of them.

If it is impossible to find a rally point which can be reached by all heroes, print a single integer -1 in the output.

Examples

Input

8 3
8 2
1 3
4 9
0 3 -5 0 -5 -4 -1 0


Output

6
3 1 2 

Input

1 1
1 1
0


Output

1
1 

Input

3 2
1 1
3 1
0 -5000 0


Output

-1


Input

8 3
1 15
5 10
8 1
0 -5 -5 -5 0 -5 -5 0


Output

7
2 1 3 

Note

The picture illustrates the first example:

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.Closeable;
import java.io.DataInputStream;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			long startTime = System.currentTimeMillis();
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			FastReader in = new FastReader(inputStream);
			Output out = new Output(outputStream);
			GMonstersAndPotions solver = new GMonstersAndPotions();
			solver.solve(1, in, out);
			out.close();
			System.err.println(System.currentTimeMillis()-startTime+"ms");
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<26);
		thread.start();
		thread.join();
	}

	static class GMonstersAndPotions {
		private final int iinf = 1_000_000_000;

		public GMonstersAndPotions() {
		}

		public ArrayList<Integer> solve(int[] arr, int[] ind, boolean reverse) {
			if(reverse) {
				Utilities.reverse(arr);
				Utilities.reverse(ind);
				return solve(arr, ind, false);
			}
			int n = arr.length;
			ArrayList<Integer> ret = new ArrayList<>();
			for(int i = 0; i<n; i++) {
				int start = 0;
				int min = 0;
				for(int j = 0; j<n; j++) {
					min = Math.max(0, min);
					if(arr[j]>=iinf) {
						if(arr[j]-iinf>=min) {
							min = 0;
							arr[j] = 0;
							for(int k = start; k<=j; k++) {
								if(arr[k]<iinf) {
									arr[k] = 0;
								}
							}
							start = j+1;
							ret.add(ind[j]);
						}
					}else {
						min -= arr[j];
					}
				}
			}
			return ret;
		}

		public void solve(int kase, InputReader in, Output pw) {
			int n = in.nextInt(), m = in.nextInt();
			int[] arr = new int[n];
			int[] ind = new int[n];
			for(int i = 0; i<m; i++) {
				int x = in.nextInt()-1;
				arr[x] = in.nextInt()+iinf;
				ind[x] = i+1;
			}
			for(int i = 0; i<n; i++) {
				int cur = in.nextInt();
				if(arr[i]==0) {
					arr[i] = cur;
				}
			}
			for(int i = 0; i<n; i++) {
				var l = solve(Arrays.copyOfRange(arr, 0, i+1), Arrays.copyOfRange(ind, 0, i+1), true);
				int add = l.isEmpty() ? 0 : 1;
				var r = solve(Arrays.copyOfRange(arr, i+add, n), Arrays.copyOfRange(ind, i+add, n), false);
				if(l.size()+r.size()==m) {
					pw.println(i+1);
					for(int k: l) {
						pw.print(k+" ");
					}
					for(int k: r) {
						pw.print(k+" ");
					}
					return;
				}
			}
			pw.println("-1");
		}

	}

	static interface InputReader {
		int nextInt();

	}

	static class FastReader implements InputReader {
		final private int BUFFER_SIZE = 1<<16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer;
		private int bytesRead;

		public FastReader(InputStream is) {
			din = new DataInputStream(is);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public int nextInt() {
			int ret = 0;
			byte c = skipToDigit();
			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;
		}

		private boolean isDigit(byte b) {
			return b>='0'&&b<='9';
		}

		private byte skipToDigit() {
			byte ret;
			while(!isDigit(ret = read())&&ret!='-') ;
			return ret;
		}

		private void fillBuffer() {
			try {
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			}catch(IOException e) {
				e.printStackTrace();
				throw new InputMismatchException();
			}
			if(bytesRead==-1) {
				buffer[0] = -1;
			}
		}

		private byte read() {
			if(bytesRead==-1) {
				throw new InputMismatchException();
			}else if(bufferPointer==bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public String lineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			lineSeparator = System.lineSeparator();
		}

		public void print(String s) {
			sb.append(s);
			if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println(int i) {
			println(String.valueOf(i));
		}

		public void println(String s) {
			sb.append(s);
			println();
		}

		public void println() {
			sb.append(lineSeparator);
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}

	static class Utilities {
		public static void swap(int[] arr, int i, int j) {
			if(i!=j) {
				arr[i] ^= arr[j];
				arr[j] ^= arr[i];
				arr[i] ^= arr[j];
			}
		}

		public static void reverse(int[] arr, int i, int j) {
			while(i<j) {
				swap(arr, i++, j--);
			}
		}

		public static void reverse(int[] arr) {
			reverse(arr, 0, arr.length-1);
		}

	}
}