Problem: Ivan is going to sleep now and wants to set his alarm clock. There will be many necessary events tomorrow, the i-th of them will start during the x_i-th minute. Ivan doesn't want to skip any of the events, so he has to set his alarm clock in such a way that it rings during minutes x_1, x_2, ..., x_n, so he will be awake during each of these minutes (note that it does not matter if his alarm clock will ring during any other minute).

Ivan can choose two properties for the alarm clock — the first minute it will ring (let's denote it as y) and the interval between two consecutive signals (let's denote it by p). After the clock is set, it will ring during minutes y, y + p, y + 2p, y + 3p and so on.

Ivan can choose any minute as the first one, but he cannot choose any arbitrary value of p. He has to pick it among the given values p_1, p_2, ..., p_m (his phone does not support any other options for this setting).

So Ivan has to choose the first minute y when the alarm clock should start ringing and the interval between two consecutive signals p_j in such a way that it will ring during all given minutes x_1, x_2, ..., x_n (and it does not matter if his alarm clock will ring in any other minutes).

Your task is to tell the first minute y and the index j such that if Ivan sets his alarm clock with properties y and p_j it will ring during all given minutes x_1, x_2, ..., x_n or say that it is impossible to choose such values of the given properties. If there are multiple answers, you can print any.

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 3 ⋅ 10^5, 1 ≤ m ≤ 3 ⋅ 10^5) — the number of events and the number of possible settings for the interval between signals.

The second line of the input contains n integers x_1, x_2, ..., x_n (1 ≤ x_i ≤ 10^{18}), where x_i is the minute when i-th event starts. It is guaranteed that all x_i are given in increasing order (i. e. the condition x_1 < x_2 < ... < x_n holds).

The third line of the input contains m integers p_1, p_2, ..., p_m (1 ≤ p_j ≤ 10^{18}), where p_j is the j-th option for the interval between two consecutive signals.

Output

If it's impossible to choose such values y and j so all constraints are satisfied, print "NO" in the first line.

Otherwise print "YES" in the first line. Then print two integers y (1 ≤ y ≤ 10^{18}) and j (1 ≤ j ≤ m) in the second line, where y is the first minute Ivan's alarm clock should start ringing and j is the index of the option for the interval between two consecutive signals (options are numbered from 1 to m in the order they are given input). These values should be chosen in such a way that the alarm clock will ring during all given minutes x_1, x_2, ..., x_n. If there are multiple answers, you can print any.

Examples

Input


3 5
3 12 18
2 6 5 3 3


Output


YES
3 4


Input


4 2
1 5 17 19
4 5


Output


NO


Input


4 2
1 5 17 19
2 1


Output


YES
1 1

Solution (in JAVA):

Solution:
import java.io.*;
import java.text.DecimalFormat;
import java.util.*;
public class l {
    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMMMM      MMMMMM      OOO      OOO        SSSS   SSS     EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEE           MMMM MMM  MMM MMMM    OOO          OOO    SSSS       SSS   EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM  MMMMMM  MMMM   OOO            OOO   SSSS             EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM  OOO              OOO   SSSSSSS         EEEEE          /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO      SSSSSS       EEEEEEEEEEE    /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO         SSSSSSS   EEEEEEEEEEE    /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM   OOO            OOO              SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM    OOO          OOO     SSS       SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM      OOO      OOO        SSS    SSSS    EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    static int mod = (int) (1e9 + 7);
    static int n;
    static StringBuilder sol;

    static class pair implements Comparable<pair> {
        int val, cost;

        public pair(int x, int y) {
            val = x;
            cost = y;
        }

        public int compareTo(pair o) {
            if (o.val == val) return cost - o.cost;
            return val - o.val;
        }

        public String toString() {
            return val + " " + cost;
        }
    }

    static class tri implements Comparable<tri> {
        int lef, righ, idx;

        tri(int a, int b, int c) {
            lef = a;
            righ = b;
            idx = c;
        }

        public int compareTo(tri o) {
            if (lef == o.lef) return righ - o.righ;
            return lef - o.lef;
        }

        public String toString() {
            return lef + " " + righ + " " + idx;
        }
    }
    static ArrayList<Integer>[]adj;
    static boolean[]vis;
    static ArrayList<Integer>ans;
    static void dfs(int u){
        vis[u]=true;
        ans.add(u+1);
        for (int v:adj[u]){
            if (!vis[v])dfs(v);
        }
    }

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        //FileWriter f = new FileWriter("C:\\Users\\Ibrahim\\out.txt");
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int m = sc.nextInt();
        long start= -1;
        long g =0;
        long pre=-1;
        for (int i =0;i<n;i++){
            long x = sc.nextLong();
            if (start==-1){
                start=x;
                pre=x;
            }
            g=gcd(g,x-pre);
            pre=x;
        }
        //pw.println(g);
        for (int j =1;j<=m;j++){
            long z = sc.nextLong();
            if (g%z==0){
                pw.println("YES");
                pw.println(start+" "+j);
                pw.flush();
                return;
            }
        }
        pw.println("NO");
        pw.flush();
    }
    static long gcd(long a ,long b){
        if (a==0)return b;
        return gcd(b%a,a);
    }

    static final int R = 26;                //Alphabet (lowercase etters in below implementation)

    static class Node {
        Node[] next = new Node[R];
        int val = -1;
        int count=0;
    }

    static Node root ;
    static int[]mm;
    static void put(char[] s, int idx)        // O(n) where n = |s|. Can be implemented recursively
    {
        Node cur = root;
        int i =1;
        for (char c : s) {
            Node nxt = cur.next[c - 'a'];
            if (nxt == null)
                nxt = cur.next[c - 'a'] = new Node();
            cur = nxt;
            cur.count++;
            mm[i]=Math.max(mm[i],cur.count);
            i++;
        }
        cur.val = idx;
    }

    static int search(char[] s) {
        Node cur = root;
        for (char c : s) {
            Node nxt = cur.next[c - 'a'];
            if (nxt == null)
                return -1;
            cur = nxt;
        }
        return cur.val;
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}