Problem:
Score : 900 points

Problem Statement

There are N robots and M exits on a number line.
The N + M coordinates of these are all integers and all distinct.
For each i (1 \leq i \leq N), the coordinate of the i-th robot from the left is x_i.
Also, for each j (1 \leq j \leq M), the coordinate of the j-th exit from the left is y_j.

Snuke can repeatedly perform the following two kinds of operations in any order to move all the robots simultaneously:

Increment the coordinates of all the robots on the number line by 1.

Decrement the coordinates of all the robots on the number line by 1.

Each robot will disappear from the number line when its position coincides with that of an exit, going through that exit.
Snuke will continue performing operations until all the robots disappear.

When all the robots disappear, how many combinations of exits can be used by the robots?
Find the count modulo 10^9 + 7.
Here, two combinations of exits are considered different when there is a robot that used different exits in those two combinations.

Constraints

1 \leq N, M \leq 10^5

1 \leq x_1 < x_2 < ... < x_N \leq 10^9

1 \leq y_1 < y_2 < ... < y_M \leq 10^9

All given coordinates are integers.

All given coordinates are distinct.

Input

Input is given from Standard Input in the following format:

N M
x_1 x_2 ... x_N
y_1 y_2 ... y_M

Output

Print the number of the combinations of exits that can be used by the robots when all the robots disappear, modulo 10^9 + 7.

Sample Input 1

2 2
2 3
1 4

Sample Output 1

3

The i-th robot from the left will be called Robot i, and the j-th exit from the left will be called Exit j.
There are three possible combinations of exits (the exit used by Robot 1, the exit used by Robot 2) as follows:

(Exit 1, Exit 1)

(Exit 1, Exit 2)

(Exit 2, Exit 2)

Sample Input 2

3 4
2 5 10
1 3 7 13

Sample Output 2

8

The exit for each robot can be chosen independently, so there are 2^3 = 8 possible combinations of exits.

Sample Input 3

4 1
1 2 4 5
3

Sample Output 3

1

Every robot uses Exit 1.

Sample Input 4

4 5
2 5 7 11
1 3 6 9 13

Sample Output 4

6

Sample Input 5

10 10
4 13 15 18 19 20 21 22 25 27
1 5 11 12 14 16 23 26 29 30

Sample Output 5

22

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.math.*;
import java.util.*;
import java.util.stream.*;

public class Main {
	
	static class Pair implements Comparable<Pair> {
		int x;
		int y;

		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			if (x != o.x) {
				return x < o.x ? -1 : 1;
			}
			return Integer.compare(y, o.y);
		}

		@Override
		public String toString() {
			return "(" + x + ", " + y + ")";
		}
	}

	void submit() {
		int n = nextInt();
		int m = nextInt();
		
		Pair[] a = new Pair[n + m];
		for (int i = 0; i < n + m; i++) {
			a[i] = new Pair(nextInt(), i < n ? 0 : 1);
		}
		Arrays.sort(a);
		
		int last = -1;
		
		int[] ls = new int[n];
		int[] rs = new int[n];
		
		int ptr = 0;
		for (Pair p : a) {
			if (p.y == 0) {
				ls[ptr++] = last == -1 ? -1 : p.x - last; 
			} else {
				last = p.x;
			}
		}
		
		last = -1;
		for (int i = a.length - 1; i >= 0; i--) {
			Pair p = a[i];
			if (p.y == 0) {
				rs[--ptr] = last == -1 ? -1 : last - p.x;
			} else {
				last = p.x;
			}
		}
		
		ArrayList<Pair> b = new ArrayList<>();
		
		for (int i = 0; i < n; i++) {
			if (ls[i] != -1 && rs[i] != -1) {
				b.add(new Pair(ls[i], -rs[i]));
			}
		}
		
		out.println(go(b));
	}
	
	int go(ArrayList<Pair> a) {
		Collections.sort(a);
		
		int[] b = new int[a.size()];
		int sz = 0;
		for (int i = 0; i < a.size(); i++) {
			if (i == 0 || a.get(i - 1).compareTo(a.get(i)) != 0) {
				b[sz++] = a.get(i).y;
			}
		}
		
		b = Arrays.copyOf(b, sz);
		
		int[] u = unique(b);
		int n = b.length;
		int m = u.length + 1;
		for (int i = 0; i < n; i++) {
			b[i] = Arrays.binarySearch(u, b[i]) + 1;
		}
		
		int[] fen = new int[m];
		
		add(fen, 0, 1);
		
		for (int i = n - 1; i >= 0; i--) {
			int x = b[i];
			
			add(fen, x, get(fen, x - 1));
		}
		
		return get(fen, m - 1);
	}
	
	static final int P = 1_000_000_007;
	
	void add(int[] fen, int idx, int delta) {
		for (int i = idx; i < fen.length; i |= i + 1) {
			fen[i] += delta;
			if (fen[i] >= P) {
				fen[i] -= P;
			}
		}
	}
	
	int get(int[] fen, int idx) {
		int ret = 0;
		for (int i = idx; i >= 0; i = (i & (i + 1)) - 1) {
			ret += fen[i];
			if (ret >= P) {
				ret -= P;
			}
		}
		return ret;
	}
	
	int[] unique(int[] a) {
		a = a.clone();
		int sz = 0;
		Arrays.sort(a);
		for (int i = 0; i < a.length; i++) {
			if (sz == 0 || a[i] != a[sz - 1]) {
				a[sz++] = a[i];
			}
		}
		return Arrays.copyOf(a, sz);
	}

	void test() {

	}

	void stress() {
		for (int tst = 0;; tst++) {
			if (false) {
				throw new AssertionError();
			}
			System.err.println(tst);
		}
	}

	Main() throws IOException {
		is = System.in;
		out = new PrintWriter(System.out);
		submit();
		// stress();
		// test();
		out.close();
	}

	static final Random rng = new Random();
	static final int C = 5;

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new Main();
	}

	private InputStream is;
	PrintWriter out;

	private byte[] buf = new byte[1 << 14];
	private int bufSz = 0, bufPtr = 0;

	private int readByte() {
		if (bufSz == -1)
			throw new RuntimeException("Reading past EOF");
		if (bufPtr >= bufSz) {
			bufPtr = 0;
			try {
				bufSz = is.read(buf);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			if (bufSz <= 0)
				return -1;
		}
		return buf[bufPtr++];
	}

	private boolean isTrash(int c) {
		return c < 33 || c > 126;
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isTrash(b))
			;
		return b;
	}

	String nextToken() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	String nextString() {
		int b = readByte();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b) || b == ' ') {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	double nextDouble() {
		return Double.parseDouble(nextToken());
	}

	char nextChar() {
		return (char) skip();
	}

	int nextInt() {
		int ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}

	long nextLong() {
		long ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}
}