Problem: 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.

Examples

Input

2 2
2 3
1 4


Output

3


Input

3 4
2 5 10
1 3 7 13


Output

8


Input

4 1
1 2 4 5
3


Output

1


Input

4 5
2 5 7 11
1 3 6 9 13


Output

6


Input

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


Output

22

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        static final int mod = (int) 1e9 + 7;

        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int[] x = in.nextIntArray(n);
            int[] y = in.nextIntArray(m);

            int posLen = 0;
            int lrLen = 0;
            int[] pos = new int[2 * n + 1];
            int[][] lr = new int[n][2];
            pos[posLen++] = 0;
            for (int i = 0; i < n; i++) {
                int idx = Arrays.binarySearch(y, x[i]);
                idx = -idx - 2;
                if (idx < 0 || idx + 1 >= m) continue;
                lr[lrLen][0] = x[i] - y[idx];
                lr[lrLen][1] = y[idx + 1] - x[i];
                pos[posLen++] = lr[lrLen][0];
                pos[posLen++] = lr[lrLen][1];
                lrLen++;
            }
            pos = Arrays.copyOf(pos, posLen);
            lr = Arrays.copyOf(lr, lrLen);
            Arrays.sort(pos);
            for (int[] p : lr) {
                p[0] = Arrays.binarySearch(pos, p[0]);
                p[1] = Arrays.binarySearch(pos, p[1]);
            }
            Arrays.sort(lr, (a, b) -> {
                if (a[1] != b[1]) return a[1] - b[1];
                return -(a[0] - b[0]);
            });

            TreeSet<Long> use = new TreeSet<>();
            BIT bit = new BIT(posLen + 1);
            bit.add(0, 1);
            for (int[] p : lr) {
                if (!use.add((long) p[0] << 32 | p[1])) continue;
                bit.add(p[0], bit.sum(p[0]));
            }
            out.println(bit.sum(posLen + 1));
        }

        class BIT {
            final int n;
            final long[] bit;

            public BIT(int size) {
                n = size;
                bit = new long[n + 1];
            }

            public long sum(int i) {
                long res = 0;
                for (; i > 0; i -= i & -i) {
                    res += bit[i];
                    while (res >= mod) res -= mod;
                }
                return res;
            }

            public void add(int i, long x) {
                i++;
                for (; i <= n; i += i & -i) {
                    bit[i] += x;
                    while (bit[i] >= mod) bit[i] -= mod;
                }
            }

        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

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

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}